$10 000 is invested at a rate of 10% per annum compounding half yearly.
The value, in dollars, of this investment after five years, is given by
- `10\ 000 xx 0.10 xx 5`
- `10\ 000 xx 0.05 xx 10`
- `10\ 000 xx 0.05^10`
- `10\ 000 xx 1.05^10`
Aussie Maths & Science Teachers: Save your time with SmarterEd
$10 000 is invested at a rate of 10% per annum compounding half yearly.
The value, in dollars, of this investment after five years, is given by
`D`
`text(Interest rate)\ (r) = \frac{10%}{2} = \frac{0.10}{2} = 0.05\ \ \text{(per 6 months)}`
`text{Compounding periods}\ (n) =5 xx 2=10`
`FV` | ` = PV(1+r)^n` |
`= 10\ 000 xx (1+0.05)^(10)` | |
`=10\ 000(1.05)^10` |
`=> D`
The points on the graph below show the balance of an investment at the start of each quarter for a period of six years.
The same rate of interest applied for these six years.
In relation to this investment, which one of the following statements is true?
`A`
`text{By elimination:}`
`text{From the graph, as balance increases after each year, interest is}`
`text{credited annually (eliminate B and D).}`
`text{The difference of the balances between successive years is increasing}`
`text{which indicates that interest is compounding (eliminate D).}`
`=> A`
Callum invests $20 000 in a term deposit account that adds 3.8% interest annually, calculated on the account balance at the end of each year.
Calculate the interest paid in the third year of Callum's investment. (3 marks)
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`$818.86`
`r=3.8% = 0.038`
`text(Using)\ \ FV=PV(1+r)^n :`
`text(Value after 2 years)` | `= 20\ 000(1.038)^2` |
`= $21\ 548.88` | |
`text(Value after 3 years)` | `= 20\ 000(1.038)^3` |
`= $22\ 367.74` |
`:.\ text(Interest paid in 3rd year)` | `= 22\ 367.74-21\ 548.88` |
`= $818.86` |
Tim invests $3000 in a term deposit account that adds 6.5% interest annually, calculated on the account balance at the end of each year.
The interest paid in the fourth year is
`B`
`r=6.5% = 0.065`
`text(Using)\ \ FV=PV(1+r)^n :`
`text(Value after 3rd year)` | `= 3000(1.065)^3` |
`= $3623.85` | |
`text(Value after 4th year)` | `= 3000(1.065)^4` |
`= $3859.40` |
`:.\ text(Interest paid in 4th year)` | `= 3859.40-3623.85` |
`= $235.55` |
`=> B`
Kelly invests $8 000 at an interest rate of 7.5% per annum, compounding annually.
After how many years will her investment first be more than double its original value, giving your answer to the nearest year? (3 marks)
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`10\ text{years}`
`FV=PV(1+r)^n`
`r=7.5% = 0.075, PV=8000`
`text(Find)\ n\ text(when)\ FV>16\ 000:`
`8000(1+0.075)^n` | `> 16\ 000` |
`1.075^n` | `> 2` |
`text(Testing possible values:)`
`1.075^10 = 2.06`
`1.075^9 = 1.92`
`:.\ \text{Kelly’s investment will first double after 10 years.}`
Gerry invests $10 000 at an interest rate of 5.5% per annum, compounding annually.
After how many years will his investment first be more than double its original value?
`B`
`FV=PV(1+r)^n`
`r=5.5% = 0.055, PV=10\ 000`
`text(Find)\ n\ text(when)\ FV>20\ 000:`
`10\ 000(1+0.055)^n` | `> 20\ 000` |
`1.055^n` | `> 2` |
`text(Test answer options:)`
`1.055^12 = 1.90`
`1.055^13 = 2.005`
`=> B`
Ekamjot invests $13 000 for two years.
Interest is calculated at the rate of 7.2% per annum, compounding quarterly.
How much interest does Ekamjot earn from this investment, giving your answer to the nearest cent? (2 marks)
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`$1994.28`
`text{Annual interest rate}\ = 7.2% = 0.072`
`text(Quarterly interest rate)\ (r) = \frac{0.072}{4} = 0.018`
`text(Compounding periods)\ (n) = 2 xx 4 =8`
`FV(text{after 2 years})` | `= PV(1+r)^n` |
`=13\ 000(1 + 0.018)^8` | |
`=$14\ 994.278….` | |
`=$14\ 994.28` |
`text{Interest earned}\ =14\ 994.28-13\ 000=$1994.28`
Mary invests $1200 for two years.
Interest is calculated at the rate of 3.35% per annum, compounding monthly.
The amount of interest she earns in two years is closest to
`D`
`text{Annual interest rate}\ = 3.35% = 0.0335`
`text(Monthly interest rate)\ (r) = \frac{0.0335}{12}`
`text(Compounding periods)\ (n) = 2 xx 12 =24`
`FV(text{after 2 years})` | `= PV(1+r)^n` |
`=1200(1 + \frac{0.0335}{12})^24` | |
`=$1283.03…` |
`text{Interest earned}\ =1283.03-1200=$83.03`
`=> D`
Amy invests $15 000 for 150 days.
Interest is calculated at the rate of 4.60% per annum, compounding daily.
Assuming that there are 365 days in a year, find the value of her investment after 150 days, giving your answer to the nearest dollar. (3 marks)
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`$15\ 286`
`text{Annual interest rate}\ =4.60%=0.046`
`text{Daily interest rate}\ = \frac{0.046}{365}`
`FV` | `= 15\ 000 xx (1 + \frac{0.046}{365})^150` |
`= 15\ 000 xx (1.000126…)^150` | |
`= 15\ 000 xx (1.01908…)` | |
`= $15\ 286\ \ \text{(nearest dollar)}` |
Sam and Charlie each invest $5000 for three years.
Sam’s investment earns simple interest at the rate of 7.5% per annum.
Charlie’s investment earns interest at the rate of 7.5% per annum compounding annually.
At the conclusion of three years, determine which investment has the highest value and by how much. (4 marks)
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`text{Charlie’s investment is worth $86.48 more than Sam’s.}`
`text(Sam’s Investment:)`
`I=Prn = 5000 xx \frac{7.5}{100} xx 3 = $1125`
`text{Investment value}\ = 5000 + 1125 = $6125`
`text(Charlie’s Investment:)`
`FV` | `= PV(1+r)^n` |
`= 5000 xx 1.075^3` | |
`= $6211.48` |
`text{Difference}\ = 6211.48-6125= $86.48`
`:.\ \text{Charlie’s investment is worth $86.48 more than Sam’s.}`
What amount must be invested now at 6% per annum, compounded quarterly, so that in eighteen months it will have grown to `$14\ 000`? Give your answer to the nearest cent. (2 marks)
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`$12\ 803.59`
`\text{Interest rate}\ (r) = \frac{0.06}{4} = 0.015\ \ \text{(per quarter)}`
`\text{Compounding periods}\ (n) = \frac{18}{3} = 6`
`FV` | `=PV(1+r)^n` |
`14\ 000` | `= PV(1 + 0.015)^(6)` |
`:.PV` | `= (14\ 000)/1.015^(6)` |
`= $12\ 803.59` |
Louise's investment earns 3.6% per annum, compounded quarterly.
She calculates that her investment will be worth $7400 in 4 years.
Determine the amount that Louise initially invests, giving your answer to the nearest cent. (2 marks)
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`$6411.70`
`\text{Interest rate}\ (r) = \frac{0.036}{4} = 0.009\ \ \text{(per quarter)}`
`\text{Compounding periods}\ (n) = 4 xx 4 = 16`
`FV` | `=PV(1+r)^n` |
`7400` | `= PV(1 + 0.009)^(16)` |
`:.PV` | `= \frac{7400}{1.009^{16}}` |
`= $6411.70\ \ \text{(nearest cent)}` |
Marshall's investment earns 5% per annum, compounded annually.
He calculates that his investment will be worth $1100 in 3 years, to the nearest dollar.
The amount Marshall invests now is closest to
`C`
`FV = PV(1 + r)^n`
`r` | `=\ text(5%)` | `= 0.05\ text(per annum)` |
`n` | `=3` |
`1100` | `= PV(1 + 0.05)^(3)` |
`:.PV` | `= \frac{1100}{1.05^{3}}` |
`= $950` |
`=> C`
A bank's Compound Saver Account pays interest at 4% per annum, compounded quarterly.
Sacha deposits $6500 when he opens his Compound Saver Account and makes no further deposits or withdrawals.
What will be the balance in the account at the end of 1.5 years, to the nearest dollar? (2 marks)
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`$6900`
`text{Compounding periods}\ (n) =1.5 xx 4=6`
`text{Compounding rate}\ (r) = \frac{0.04}{4} = 0.01`
`FV` | `= PV(1 + r)^n` |
`= 6500(1 + 0.01)^6` | |
`= 6899.88…` | |
`=$6900\ \ \text{(nearest dollar)}` |
Jill opens a Smartsave Account that pays interest at 5% per annum, compounded quarterly.
Jill deposits $700 when she opens the account and makes no further deposits or withdrawals.
What will be the balance in the account at the end of 3 years, to the nearest dollar? (2 marks)
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`$813`
`text{Compounding periods}\ (n) =3 xx 4=12`
`text{Compounding rate}\ (r) = \frac{0.05}{4} = 0.0125`
`FV` | `= PV(1 + r)^n` |
`= 700(1 + 0.0125)^12` | |
`= 812.528…` | |
`=$813\ \ \text{(nearest dollar)}` |
A bank's Maxi Saver Account pays interest at 6% per annum, compounded quarterly.
Jen opens a Maxi Saver Account and deposits $3000 into it.
Assuming no further deposits or withdrawals are made, what will be the balance in the account at the end of two years?
`=> C`
`text{Compounding periods}\ (n) =2 xx 4=8`
`text{Compounding rate}\ (r) = \frac{0.06}{4} = 0.015`
`FV` | `= PV(1 + r)^n` |
`= 3000(1 + 0.015)^8` | |
`= $3379.48` |
`=> C`
Shannon invests $25 000 in an account that earns interest at 6% per annum, compounded monthly.
What is the future value of Shannon's investment, to the nearest dollar, after 2 years? (2 marks)
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`$28\ 179`
`text{Annual interest rate = 6.0% = 0.06}`
`text(Monthly interest rate) = \frac(0.06)(12) = 0.005`
`n = 2 xx 12 = 24`
`FV` | `= PV(1 + r)^n` |
`= 25\ 000 (1 + 0.005)^24` | |
`= 28\ 178.99` | |
`=$28\ 179\ \ \text{(nearest dollar)}` |
Natalie is saving for a netball hoop and invests $2200 in an account that earns interest at 5.5% per annum, compounded monthly.
What is the future value of Natalie's investment, to the nearest dollar, after 1.5 years? (2 marks)
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`$2389`
`text{Annual interest rate = 5.5% = 0.055}`
`text(Monthly interest rate) = \frac(0.055)(12)`
`n = 1.5 xx 12 = 18`
`FV` | `= PV(1 + r)^n` |
`= 2200 (1 + frac(0.055)(12))^18` | |
`= 2388.74…` | |
`=$2389` |
Roger invests $1400. He earns interest at 4% per annum, compounded monthly.
What is the future value of Roger's investment after 2.5 years?
`B`
`text{Annual interest rate = 4% = 0.04}`
`text(Monthly interest rate) = \frac(0.04)(12)`
`n = 2.5 xx 12 = 130`
`FV` | `= PV(1 + r)^n` |
`= 1400 (1 + frac(0.04)(12))^30` | |
`= $1546.98` |
`=> \ B`
In Japan, a bowl of ramen cost 1000 Japanese yen in 2005. The cost of ramen has increased by 0.5% per annum since then.
Determine the cost of the same bowl of ramen in 2020 in Japanese yen, to the nearest yen. (2 marks)
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`1078\ text{yen}`
`r =\ text(0.5%)\ = 0.005`
`n = 15\ text(years)`
`FV` | `=PV(1+r)^n` | |
`=1000(1 + 0.005)^15` | ||
`=1077.68…` | ||
`=1078\ text{yen}` |
At the pump, one litre of diesel fuel cost 98 cents in NSW in 2003. The value of diesel fuel has increased by 4% per annum since then.
Which expression gives the value, in cents, of one litre of diesel at the pump in 2023?
`B`
`r =\ text(4%)\ = 0.04`
`n = 20\ text(years)`
`text{Using}\ \ FV=PV(1+r)^n`
`text{Value in 2023} =98(1 + 0.04)^20`
`=> B`
Samanda opens a bank account and deposits $5000 into it. Interest is paid at 4% per annum, compounding annually.
Assuming no further deposits or withdrawals are made, what will be the balance in the account at the end of three years? (2 marks)
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`$5624.32`
`FV` | `= PV(1 + r)^n` |
`= 5000(1 + 0.05)^3` | |
`= $5624.32` |
Resilia opens a bank account and deposits $2000 into it. Interest is paid at 4% per annum, compounding annually.
Assuming no further deposits or withdrawals are made, what will be the balance in the account at the end of two years?
`=> B`
`FV` | `= PV(1 + r)^n` |
`= 2000(1 + 0.04)^2` | |
`= $2163.20` |
`=> B`
Jevin has a bank account that pays him simple interest.
The bank statement below shows the transactions on Jevin’s account for the month of July.
--- 1 WORK AREA LINES (style=lined) ---
Interest for this account is calculated on the minimum monthly balance at a rate of 3.0% per annum.
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a. | `text(Deposit)` | `= 6870.67-6250.67` |
`= $620` |
b. `text(Minimum Balance) = $6120.86`
`I` | `=Prn` |
`= 6120.86 xx 3/100 xx 1/12` | |
`= 15.302…` | |
`= $15.30` |
The transaction details for a savings account for the month of August 2014 are shown in the table below.
The table is incomplete.
Simple interest is calculated and paid monthly on the minimum balance for that month.
Calculate the annual simple interest rate paid on this account, correct to two decimal places. (4 marks)
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`text{3.75%}`
`text(Minimum balance for month) = $4870.50`
`text{Interest paid}\ = 5885.72-5870.50= $15.22`
`I` | `=Prn` |
`15.22` | `= 4870.50 xx r xx 1/12` |
`:. r` | `=(15.22 xx 12)/4870.50` |
`= 0.03749…` | |
`= 3.75text{% (2 d.p.)}` |
The graph below shows the growth in value of a $1000 investment over a period of four years.
A different amount of money is invested under the same investment conditions for eight years.
In total, the amount of interest earned on this investment is $600.
Calculate the amount of money invested. (3 marks)
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`$1500`
`text(The linear graph shows a simple interest rate is applied.)`
`text{Simple interest rate} = 50/1000 xx 100=5text(% p.a.)`
`I = 600,\ \ r = 5/100,\ \ n=8`
`600` | `= P xx 5/100 xx 8` |
`:.P` | `= 600/0.4` |
`= $1500` |
Chardie invests a sum of money in an account paying simple interest at a rate of 5.25% per annum.
No withdrawals or deposits are made into the account and over 4 years and the total value of Chardie's investment grows to `$22\ 385`.
Calculate the sum of money Chardie originally invested. (3 marks)
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`$18\ 500`
`text{Interest earned}\ = 22\ 385-18\ 500=$3885`
`I = 3885, \ \ r = 5.25/100, \ \ n = 4`
`I` | `= Prn` |
`3885` | `= P xx 5.25/100 xx 4` |
`P` | `= 3885/0.21` |
`= $18\ 500` |
A sum of money is invested in an account paying simple interest at a rate of 5.0% per annum.
No withdrawals or deposits are made into the account and over 3 years, with the total interest earned on the investment being $120.
Calculate the sum of money originally invested. (2 marks)
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`$800`
`I = 120, \ \ r = 5/100, \ \ n = 3`
`I` | `= Prn` |
`120` | `= P xx 5/100 xx 3` |
`P` | `= 120/0.15` |
`= $800` |
Wilbur invests a sum of money into an account paying simple interest at a rate of 4.25% per annum.
The total interest earned on Wilbur's investment over 4 years is $6800.
Calculate the sum of money Wilbur originally invested. (2 marks)
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`$40\ 000`
`I = 6800, \ \ r = 4.25/100, \ \ n = 4`
`I` | `= Prn` |
`6800` | `= P xx 4.25/100 xx 4` |
`P` | `= 6800/0.17` |
`= $40\ 000` |
A sum of money is invested in an account paying simple interest at a rate of 8% per annum.
The total interest earned on this investment over 6 years is $27 000.
The sum of money invested is
`C`
`I = 27 \ 000, \ \ r = 8/100, \ \ n = 6`
`I` | `= Prn` |
`27 \ 000` | `= (P xx 8 xx 6)/100` |
`P` | `= (2\ 700\ 000)/48` |
`= $56\ 250` |
`=> C`
Kate and Amberley are Swifties and want to travel to Melbourne to go to a Tay-Tay concert.
It will cost them a total of $13 000 for tickets, accommodation and transport.
They currently have $12 500 and can invest this amount for 9 months.
What is the minimum simple interest rate, correct to 1 decimal place, at which they can invest their money to reach their goal of $13 000? (3 marks)
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`5.4\text{%}`
`n = \frac {9}{12} = 0.75`
`text{Interest required to reach goal} =13\ 000-12\ 500=$500`
`I` | `=Prn` |
`500` | `=12\ 500 xx r xx 0.75` |
`r` | `=500/9375` |
`=0.05333…` | |
`=5.333…\text{%}` |
`:.\ text{Minimum interest rate = 5.4%}`
Carissa borrowed $4000 to buy new surfboards.
She did not make any monthly repayments and repaid the loan in full 2 years later with a lump sum of $4400.
Determine the annual simple interest rate that Carissa was charged. (2 marks)
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`5.0\text{%}`
`text(Total interest paid)=4400-4000=$400`
`I` | `=Prn` |
`400` | `=4000 xx r xx 2` |
`r` | `=400/8000` |
`=0.05` | |
`=5.0\text{%}` |
Steffi borrowed $8600 to buy a new car.
She did not make any monthly repayments but instead repaid the loan in full 2 years later with a lump sum of $10 062.
Determine the annual simple interest rate that Steffi was charged. (2 marks)
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`8.50\text{%}`
`text(Total interest paid)=10\ 062-8600=$1462`
`I` | `=Prn` |
`1462` | `=8600 xx r xx 2` |
`r` | `=1462/(17\ 200)` |
`=0.0850` | |
`=8.50\text{%}` |
$2800 is invested in an account that earns simple interest at the rate of 4.0% per annum.
Calculate the total interest earned in the first six months. (2 marks)
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`$56`
`P = 2800,\ \ r = 4.0text(%),\ \ n = \frac{6}{12}=0.5`
`I` | `= Prn` |
`= 2800 xx 4.0/100 xx 0.5` | |
`= $56` |
$5000 is invested in an account that earns simple interest at the rate of 3.0% per annum.
Calculate the total interest earned in the first two years. (2 marks)
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`$300`
`P = 5000,\ \ r = 3.0text(%),\ \ n = 2`
`I` | `= Prn` |
`= 5000 xx 3.0/100 xx 2` | |
`= $300` |
Find an expression for the total value of an investment, in dollars, if $24 000 is invested for `x` months at a simple interest rate of 4.75% per annum? (2 marks)
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`$(24\ 000 + 95x)`
`text(Interest)` | `= 24\ 000 xx x/12 xx 4.75/100` |
`= 95x` |
`:.\ \text{Investment value}\ =$(24\ 000 + 95x)`
What is the interest earned, in dollars, if $4800 is invested for `x` months at a simple interest rate of 2.25% per annum?
`A`
`text(Interest)` | `= 4800 xx x/12 xx 2.25/100` |
`= 9x` |
`=> A`
Albert borrowed $2000 off his brother Sid so he could attend the rugby league Magic Round in Brisbane.
He did not make any monthly repayments but instead repaid the loan in full 12 months later with a lump sum of $2350.
What was the annual simple interest rate Sid charged Albert?
`B`
`text(Total interest paid)=2350-2000=$350`
`I` | `=Prn` |
`350` | `=2000 xx r xx 1` |
`r` | `=350/2000` |
`=0.1750` | |
`=17.50\text{%}` |
`=> B`
Sandy borrowed $7 000 for an overseas trip.
She did not make any monthly repayments but instead repaid the loan in full at the end of three years with a lump sum of $8800.
Calculate the annual simple interest rate was she charged? (2 marks)
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`8.57\text{%}`
`text(Total interest paid)=8800-7000=$1800`
`I` | `=Prn` |
`1800` | `=7000 xx r xx 3` |
`r` | `=1800/(21\ 000)` |
`=0.08571…` | |
`=8.57\text{%}` |
Jackie invests $4350 for 3 years. The simple interest is calculated at a rate of 4.5% per annum.
What is the total value of the investment at the end of this period, to the nearest dollar?
`D`
`text(Interest)` | `=Prn` |
`=4350 xx \frac{4.5}{100} xx 3` | |
`=$587.25` |
`:.\ text(Value of Investment)=4350 + 587 =$4937`
`=> D`
Gutho invests $10 000 for 1 year and 8 months. The simple interest is calculated at a rate of 4.25% per annum.
What is the total value of the investment at the end of this period, to the nearest dollar?
`C`
`text{1 year 8 months = 12 + 8 = 20 months}`
`text(Interest)` | `=Prn` |
`=10\ 000 xx \frac{4.25}{100} xx \frac{20}{12}` | |
`=$708` |
`:.\ text(Value of Investment)=10\ 000+708=$10\ 708`
`=> C`
Johnno lives overseas and needs $6000 for his planned trip to Parramatta Stadium to watch Junior Paolo play.
If he invests $5600 for 15 months at a simple interest rate of 6.5% per annum, determine if will get to see the big fella play. Show your working. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
`text(Interest)` | `=Prn` |
`=5600 xx \frac{6.5}{100} xx \frac{15}{12}` | |
`=$455` |
`text(Value of Investment)` | `=5600+455` |
`=$6055>$6000` |
`:.\ \text{Johnno will get to see Junior play}.`
`text(Interest)` | `=Prn` |
`=5600 xx \frac{6.5}{100} xx \frac{15}{12}` | |
`=$455` |
`text(Value of Investment)` | `=5600+455` |
`=$6055` |
`:.\ \text{Johnno will get to see Junior play}.`
Clancy estimates that he will need $7800 for his planned trip to visit the The Stockman's Hall of Fame in Longreach.
If he invests $7000 for 18 months at a simple interest rate of 6% per annum, will he reach his goal of $7800? Show your working. (2 marks)
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`A`
`text(Interest)` | `=Prn` |
`=7000 xx \frac{6}{100} xx \frac{18}{12}` | |
`=$630` |
`text(Value of Investment)` | `=7000+630` |
`=$7630` |
`:.\ \text{Clancy won’t reach his goal of $7800}.`
Min Woo invests $8000 for 3 years. The simple interest is calculated at a rate of 4% per annum.
Calculate the total value of the investment at the end of this period. (2 marks)
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`$8960`
`text(Interest)` | `=Prn` |
`=8000 xx \frac{4}{100} xx 3` | |
`=$960` |
`:.\ text(Value of Investment)` | `=8000+960` |
`=$8960` |
$2500 is invested in an account that earns simple interest at the rate of 3.0% per annum.
The total interest earned in the first two years is
`C`
`P = 2500,\ \ r = 3.0text(%),\ \ n = 2`
`I` | `= Prn` |
`= 2500 xx 3.0/100 xx 2` | |
`= $150` |
`=> C`
$14 000 is invested in an account that earns simple interest at the rate of 2.5% per annum.
Calculate the total interest earned in the first three years. (2 marks)
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`$1050`
`P = 14\ 000,\ \ r = 2.5text(%),\ \ n = 3`
`I` | `= Prn` |
`= 14\ 000 xx 2.5/100 xx 3` | |
`= $1050` |
The cash price of a large refrigerator is $2000.
A customer buys the refrigerator under a hire-purchase agreement.
She does not pay a deposit and will pay $55 per month for four years.
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i. `text{Total amount paid} = 55 xx 4 xx 12 = $2640`
ii. `text{Total interest} = 2640-2000= $640`
Shaun decides to buy a new sound system on a hire-purchase plan.
The sound system is priced at $3500.
Shaun pays a 15% deposit and monthly repayments for five years.
If Shaun's total purchase price after paying the last instalment is $4425, calculate his monthly repayment. (3 marks)
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`$65`
`text{Deposit} = \frac{15}{100} xx 3500 = $525`
`text{Balance due after deposit} = 4425-525= $3900`
`text{Number of repayments} = 5 xx 12 = 60`
`text{Monthly repayment} = \frac{3900}{60} = $65`
Brad investigated the cost of buying a $720 washing machine under a hire purchase agreement.
A 25% deposit is required and the balance will be paid in 24 equal monthly repayments of $27.90.
Calculate the amount of interest Brad pays on this purchase. (3 marks)
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`$129.60`
`text{Deposit} = \dfrac{25}{100} xx 720 = $180`
`text{Total instalments} = 24 xx 27.90 = $669.60`
`text{Total purchase price} = 180+669.60 = $849.60`
`text{Interest paid} = 849.60-720= $129.60`
A $2000 lounge suite was sold under a hire-purchase agreement.
A deposit of $200 was paid.
The balance was to be paid in 36 equal monthly instalments of $68.
Calculate the total interest paid in the purchase. (3 marks)
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`$648`
`text{Deposit} = $200`
`text(Total instalments) = 36 xx 68 = $2448`
`text{Total price paid} = 200 + 2448 = $2648`
`text{Interest paid} = 2648-2000 = $648`
Sandra has purchased a $4200 plasma television under a hire-purchase agreement. She paid $600 deposit and will pay the balance in equal monthly instalments of $318 over one year.
Determine the total amount of interest Sandra pays on this purchase. (3 marks)
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`$216`
`text(Deposit = $600)`
`text(Total monthly instalments) = 12 xx 318 = $3816`
`text{Total payment} = 600 + 3816 = $4416`
`text{Interest paid} = 4416-4200 = $216`
Sally purchased an electronic game machine on hire purchase. She paid $140 deposit and then $25.50 per month for two years.
What was the total amount that Sally paid? (2 marks)
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`$752`
`text(Total paid)` | `= 140 + 25.50 xx 2 xx12` |
`= $752` |
In the Venn diagram below, shade in the area that represents
`C \cup (B \cap A^{′})` (2 marks)
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In the Venn diagram below, shade in the area that represents
`(A \cap B) \cup (B \cap C) \cup (A \cap C)` (2 marks)
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In the Venn diagram below, shade in the area that represents
`(A \cap B \cap C) \cup (A \cap C^{′})` (2 marks)
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Students studying vocational education courses were surveyed about their living arrangements.
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i. `text{Number of males living with parents = 155}`
`text{Total students surveyed = 505}`
`P\text{(male and living with parents)}` | `=155/505` | |
`=0.3069…` | ||
`=31\text{% (nearest %)}` |
ii. `text{Number of females = 228}`
`text{Females not living with parents = 182}`
`P\text{(selected female not living with parents)} = 182/228 = 91/114`
A group of coalminers were surveyed about what registered vehicles they own.
They were surveyed on whether they own a car, a motorbike, both or neither and the results were recorded in the Venn diagram below.
Record this information in the partially completed 2-way table below. (2 marks)
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\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} &\ \ \ \text{Car}\ \ \ \rule[-1ex]{0pt}{0pt} & \text{No Car}\\
\hline
\rule{0pt}{2.5ex}\text{Motorbike}\rule[-1ex]{0pt}{0pt} & 7 & 8 \\
\hline
\rule{0pt}{2.5ex}\text{No Motorbike}\rule[-1ex]{0pt}{0pt} & 29 & 6 \\
\hline
\end{array}
\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} &\ \ \ \text{Car}\ \ \ \rule[-1ex]{0pt}{0pt} & \text{No Car}\\
\hline
\rule{0pt}{2.5ex}\text{Motorbike}\rule[-1ex]{0pt}{0pt} & 7 & 8 \\
\hline
\rule{0pt}{2.5ex}\text{No Motorbike}\rule[-1ex]{0pt}{0pt} & 29 & 6 \\
\hline
\end{array}
A group of 20 museum visitors were surveyed about what languages they could speak fluently.
They were surveyed on whether they could speak English or French and the results were recorded in the Venn diagram below.
Record this information in the partially completed 2-way table below. (2 marks)
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\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} & \text{English}\rule[-1ex]{0pt}{0pt} & \text{No English}\\
\hline
\rule{0pt}{2.5ex}\text{French}\rule[-1ex]{0pt}{0pt} & 5 & 3 \\
\hline
\rule{0pt}{2.5ex}\text{No French}\rule[-1ex]{0pt}{0pt} & 8 & 4 \\
\hline
\end{array}
\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} & \text{English}\rule[-1ex]{0pt}{0pt} & \text{No English}\\
\hline
\rule{0pt}{2.5ex}\text{French}\rule[-1ex]{0pt}{0pt} & 5 & 3 \\
\hline
\rule{0pt}{2.5ex}\text{No French}\rule[-1ex]{0pt}{0pt} & 8 & 4 \\
\hline
\end{array}
A class of 30 students were surveyed about their pets. They were asked whether they owned a dog, cat, both or neither and the results were recorded in the Venn diagram below.
Record this information in the partially completed 2-way table below. (2 marks)
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\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} &\ \ \ \text{Dog}\ \ \ \rule[-1ex]{0pt}{0pt} & \text{No Dog}\\
\hline
\rule{0pt}{2.5ex}\text{Cat}\rule[-1ex]{0pt}{0pt} & 3 & 7 \\
\hline
\rule{0pt}{2.5ex}\text{No Cat}\rule[-1ex]{0pt}{0pt} & 12 & 8\\
\hline
\end{array}
\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} &\ \ \ \text{Dog}\ \ \ \rule[-1ex]{0pt}{0pt} & \text{No Dog}\\
\hline
\rule{0pt}{2.5ex}\text{Cat}\rule[-1ex]{0pt}{0pt} & 3 & 7 \\
\hline
\rule{0pt}{2.5ex}\text{No Cat}\rule[-1ex]{0pt}{0pt} & 12 & 8\\
\hline
\end{array}
In the Venn diagram below, shade in the area that represents
`A \cap B \cap C` (2 marks)
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