An amount of $2500 is invested at a simple interest rate of 3% per annum.
How much interest is earned in the first two years?
- $75
- $150
- $2575
- $2652
Aussie Maths & Science Teachers: Save your time with SmarterEd
An amount of $2500 is invested at a simple interest rate of 3% per annum.
How much interest is earned in the first two years?
`B`
`I` | `=Prn` | |
`=2500 xx 3/100 xx 2` | ||
`=$150` |
`=>B`
What is the interest earned, in dollars, if $800 is invested for `x` months at a simple interest rate of 3% per annum?
`A`
`text(Interest)` | `= 800 xx x/12 xx 3/100` |
`= 2x` |
`=> A`
George makes a single deposit of $9000 into an account that pays simple interest.
After 4 years, George's account has a balance of $10 350.
What simple interest rate did George receive on his investment? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
`3.75text(%)`
`text(Interest earned)` | `= 10\ 350 – 9000` |
`= $1350` |
`text(Using)\ \ I = Prn,`
`1350` | `= 9000 xx r xx 4` |
`:. r` | `= 1350/(4 xx 9000)` |
`= 0.0375` | |
`= 3.75text(%)` |
$6000 is invested in an account that earns simple interest at the rate of 3.5% per annum.
The total interest earned in the first four years is
`D`
`P = 6000,\ \ r = 3.5text(%),\ \ n = 4`
`I` | `= Prn` |
`= 6000 xx 3.5/100 xx 4` | |
`= 840` |
`=> D`
Reece is preparing his annual budget for 2006.
His expected income is:
• $90 every week as a swimming coach
• Interest earned from an investment of $5000 at a rate of 4% per annum.
His planned expenses are:
• $30 every week on transport
• $12 every week on lunches
• $48 every month on entertainment.
Reece will save his remaining income. He uses the spreadsheet below for his budget.
--- 5 WORK AREA LINES (style=lined) ---
At the beginning of 2006, Reece starts saving.
--- 4 WORK AREA LINES (style=lined) ---
i. `text(Interest on Investment) = X`
`X` | `= 5000 xx 4 text(%)` |
`= $200` |
`text(Transport =)\ Y`
`Y` | `= 52 × 30` |
`= $1560` |
`text(Entertainment =)\ Z`
`Z` | `= 48 × 12` |
`= $576` |
ii. | `text(Total Income)` | `= 4680 + 200` |
`= $4880` |
`text(Total Expenses)` | `= 1560 + 624 + 576` |
`= $2760` |
`text(Savings)` | `= 4880 − 2760` |
`= $2120` |
`:.\ text(Reece will have saved enough for)`
`text(a $2100 deposit.)`
Lilly and Rose each have money to invest and choose different investment accounts.
The graph shows the values of their investments over time.
--- 1 WORK AREA LINES (style=lined) ---
--- 4 WORK AREA LINES (style=lined) ---
--- 2 WORK AREA LINES (style=lined) ---
`text{Rose 1 year longer (15 years) to reach the same value}`
i. `$5000\ text{(} y text(-intercept) text{)}`
ii. `text(After 6 years,)`
`text(Lilly’s investment)` | `= $9000` |
`text(Rose’s investment)` | `= $11\ 000` |
`:.\ text(Rose’s is worth $2000 more.)` |
iii. `text(It takes Lilly 14 years to reach $20 000 and it)`
`text{takes Rose 1 year longer (15 years) to reach the}`
`text(same value.)`
Lou bought a plasma TV which was priced at $3499. He paid $1000 deposit and got a loan for the balance that was paid off by 24 monthly instalments of $135.36.
What simple interest rate per annum, to the nearest percent, was charged on his loan?
(A) 11%
(B) 15%
(C) 30%
(D) 46%
`B`
`text(Loan)` | `=\ text(Price – deposit)` |
`= 3499 – 1000` | |
`= $2499` |
`text(Total repaid)` | `= 24 xx 135.36` |
`= $3248.64` |
`:.\ text(Interest paid)` | `= 3248.64\ – 2499` |
`= $749.64` |
`text(Simple Interest)` | `= Prn` |
`749.64` | `= 2499 xx r xx 2` |
`:. r` | `= 749.64/(2 xx 2499)` |
`= 0.1499…` | |
`~~15 text(%)` |
`=> B`
Minjy invests $2000 for 1 year and 5 months. The simple interest is calculated at a rate of 6% per annum.
What is the total value of the investment at the end of this period?
`A`
`text(Interest)` | `=Prn` |
`=2000 xx\ text(6%)\ xx 17/12` | |
`=$170` |
`:.\ text(Value of Investment)` | `=2000+170` |
`=$2170` |
`=> A`
Polly borrowed $11 000. She repaid the loan in full at the end of two years with a lump sum of $12 000.
What annual simple interest rate was she charged?
`B`
`text(Total interest paid)=12\ 000-11\ 000=$1000`
`I` | `=Prn` |
`1000` | `=11\ 000 xx r xx2` |
`r` | `=1000/(22\ 000)` |
`=4.55 text(%)` |
`=>\ B`
Lynne invests $1000 for a term of 15 months. Simple interest is paid on the investment at a rate of 3.75% per annum.
How much will Lynne's investment be worth at the end of the term?
`A`
`I=Prn=1000xx3.75/100xx15/12=$46.88`
`:.\ text(Investment worth)\ = 1000+46.88=$1046.88`
`=>\ A`