SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Simple Interest, SMB-023

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. What amount, in dollars, did Jevin deposit in cash on 11 July?  (1 mark)

Interest for this account is calculated on the minimum monthly balance at a rate of 3.0% per annum.

  1. Calculate the interest for July, correct to the nearest cent.  (2 marks)

Show Answers Only
  1. `$620`
  2. `$15.30`
Show Worked Solution
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`

Simple Interest, SMB-022

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)

Show Answers Only

`text{3.75%}`

Show Worked Solution

`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.)}`

Simple Interest, SMB-021

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)

Show Answers Only

`$1500`

Show Worked Solution

`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`

Simple Interest, SMB-020

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)

Show Answers Only

`$18\ 500`

Show Worked Solution

`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`

Simple Interest, SMB-019

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)

Show Answers Only

`$800`

Show Worked Solution

`I = 120, \ \ r = 5/100, \ \ n = 3`

`I` `= Prn`
`120` `= P xx 5/100 xx 3`
`P`  `= 120/0.15`
  `= $800`

Simple Interest, SMB-018

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)

Show Answers Only

`$40\ 000`

Show Worked Solution

`I = 6800, \ \ r = 4.25/100, \ \ n = 4`

`I` `= Prn`
`6800` `= P xx 4.25/100 xx 4`
`P`  `= 6800/0.17`
  `= $40\ 000`

Simple Interest, SMB-017 MC

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

  1. `$12\ 960`
  2. `$45\ 000`
  3. `$56\ 250`
  4. `$202\ 500`
Show Answers Only

`C`

Show Worked Solution

`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`

Simple Interest, SMB-016

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)

Show Answers Only

`5.4\text{%}`

Show Worked Solution

`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%}`

Simple Interest, SMB-015

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)

Show Answers Only

`5.0\text{%}`

Show Worked Solution

`text(Total interest paid)=4400-4000=$400`

`I` `=Prn`
`400` `=4000 xx r xx 2`
`r` `=400/8000`
  `=0.05`
  `=5.0\text{%}`

Simple Interest, SMB-014

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)

Show Answers Only

`8.50\text{%}`

Show Worked Solution

`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{%}`

Simple Interest, SMB-013

$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)

Show Answers Only

`$56`

Show Worked Solution

`P = 2800,\ \ r = 4.0text(%),\ \ n = \frac{6}{12}=0.5`

`I` `= Prn`
  `= 2800 xx 4.0/100 xx 0.5`
  `= $56`

Simple Interest, SMB-012

$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)

Show Answers Only

`$300`

Show Worked Solution

`P = 5000,\ \ r = 3.0text(%),\ \ n = 2`

`I` `= Prn`
  `= 5000 xx 3.0/100 xx 2`
  `= $300`

Simple Interest, SMB-011

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)

Show Answers Only

`$(24\ 000 + 95x)`

Show Worked Solution
`text(Interest)` `= 24\ 000 xx x/12 xx 4.75/100`
  `= 95x`

 
`:.\ \text{Investment value}\ =$(24\ 000 + 95x)`

Simple Interest, SMB-009 MC

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?

  1. 3.5%
  2. 17.5%
  3. 23.5%
  4. 35.0%
Show Answers Only

`B`

Show Worked Solution

`text(Total interest paid)=2350-2000=$350`

`I` `=Prn`
`350` `=2000 xx r xx 1`
`r` `=350/2000`
  `=0.1750`
  `=17.50\text{%}`

 
`=> B`

Simple Interest, SMB-008

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)

Show Answers Only

`8.57\text{%}`

Show Worked Solution

`text(Total interest paid)=8800-7000=$1800`

`I` `=Prn`
`1800` `=7000 xx r xx 3`
`r` `=1800/(21\ 000)`
  `=0.08571…`
  `=8.57\text{%}`

Simple Interest, SMB-007 MC

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?

  1. $4395
  2. $4546
  3. $4722
  4. $4937
Show Answers Only

`D`

Show Worked Solution
`text(Interest)` `=Prn`
  `=4350 xx \frac{4.5}{100} xx 3`
  `=$587.25`

 
`:.\ text(Value of Investment)=4350 + 587 =$4937`

`=>  D`

Simple Interest, SMB-006 MC

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?

  1. $10 425
  2. $10 571
  3. $10 708
  4. $14 562
Show Answers Only

`C`

Show Worked Solution

`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`

Simple Interest, SMB-005

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)

Show Answers Only
`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}.`

Show Worked Solution
`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}.`

Simple Interest, SMB-004

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)

Show Answers Only

`A`

Show Worked Solution
`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}.`

Simple Interest, SMB-003

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)

Show Answers Only

`$8960`

Show Worked Solution
`text(Interest)` `=Prn`
  `=8000 xx \frac{4}{100} xx 3`
  `=$960`

 

`:.\ text(Value of Investment)` `=8000+960`
  `=$8960`

Simple Interest, SMB-001

$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)

Show Answers Only

`$1050`

Show Worked Solution

`P = 14\ 000,\ \ r = 2.5text(%),\ \ n = 3`

`I` `= Prn`
  `= 14\ 000 xx 2.5/100 xx 3`
  `= $1050`

Financial Maths, SMB-011

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)

Show Answers Only

`3.75text(%)`

Show Worked Solution
`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(%)`

Financial Maths, SMB-009

Pamela deposits $2000 into a savings account which earns simple interest at the rate of 2.5% per annum.

No deposits or withdrawals are made from this account.

After 2 years, how much is in Pamela's savings account?  (2 marks)

Show Answers Only

`$2100`

Show Worked Solution
`text(Interest earned)` `= Prn`
  `= 2000 xx 2.5/100 xx 2`
  `= $100`

 

`:.\ text{Account balance}` `= 2000 + 100`
  `= $2100`

Financial Maths, SMB-008

Dante deposits $5000 into a savings account which earns simple interest.

No deposits or withdrawals are made from this account.

After 4 years, Dante notices there is $5600 in the account.

What is the annual rate of interest for the account?   (2 marks)

Show Answers Only

`3text(%)`

Show Worked Solution
`text(Interest per year)` `= (5600-5000)÷4`
  `= 600 ÷ 4`
  `= $150`

 

`:.\ text{Interest rate (p.a.)}` `= 150/5000 xx 100`
  `= 3 text(%)`

Financial Maths, SMB-007

Mr. Soros put $500 into a simple interest account for a year.

He did not take any money out or add any money to the account.

At the end of the year he had $530 in the account.

What was the annual percentage interest rate?   (2 marks)

Show Answers Only

`text(6%)`

Show Worked Solution
`text(Interest earned)` `= 530-500`
  `= $30`

 

`:.\ text{Interest rate (annual)}`

`= 30/500`

`= 0.06`

`= 6text(%)`

Financial Maths, SMB-006

Cassie opens a savings account and deposits $900 into it.

She makes no more deposits and earns simple interest on her original deposit at 3.5% each year.

How much interest will Cassie earn after 4 years?  (2 marks)

Show Answers Only

`$126`

Show Worked Solution
`text(Interest earned)` `=Prn`
  `= 900 xx 3.5/100 xx 4`
  `= $126`

Financial Maths, STD2 F1 2019 HSC 9 MC

What is the interest earned, in dollars, if $800 is invested for `x` months at a simple interest rate of 3% per annum?

  1. `2x`
  2. `24x`
  3. `200x`
  4. `2400x`
Show Answers Only

`A`

Show Worked Solution

♦♦♦ Mean mark 20%!

`text(Interest)` `= 800 xx x/12 xx 3/100`
  `= 2x`

 
`=> A`

Financial Maths, STD2 F1 2010 HSC 5 MC

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?

  1. $2170
  2. $2180
  3. $3003
  4. $3700
Show Answers Only

`A`

Show Worked Solution
`text(Interest)` `=Prn`
  `=2000 xx\ text(6%)\ xx 17/12`
  `=$170`

 

`:.\ text(Value of Investment)` `=2000+170`
  `=$2170`

`=>  A`

Financial Maths, STD2 F1 2013 HSC 13 MC

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?

  1. 4.17%
  2. 4.55%
  3. 8.33%
  4. 9.09%
Show Answers Only

`B`

Show Worked Solution

`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`

Financial Maths, STD2 F1 2013 HSC 9 MC

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?

  1. $1046.88
  2. $1047.09
  3. $1296.88
  4. $1468.75
Show Answers Only

`A`

Show Worked Solution

`I=Prn=1000xx3.75/100xx15/12=$46.88`

`:.\ text(Investment worth)\ = 1000+46.88=$1046.88`

`=>\ A`