joanne is investing $13600 in an account that pays 8.2% per annum, compounded monthly. A friend has agreed to sell her a second hand pick up trruck for her .........landscaping business for $15900....

joanne is investing $13600 in an account that pays 8.2% per annum, compounded monthly. A friend has agreed to sell her a second hand pick up trruck for her ...

......landscaping business for $15900. She will need to pay the government GST on the price of the truck. How long will it take, to the nearest month, to have enough in the account to buy the truck?

Asked on by islnds

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

The formula for compound interest rate is;

`FV = PV(1+i)^n`

 

FV = future value

PV = Present value

i = compound interest per month divided by 100

n = number of months

 

According to the data;

`FV = $15900`

`PV = $13600`

`n = ?`

`i = 8.2/12% = 0.683%` per month

 

`15900 = 13600(1+0.683/100)^n`

`15900/13600 =(1+0.683/100)^n`

`log(15900/13600) = log((1+0.683/100)^n)`

`0.0678 = nxxlog1.00683`

 `0.0678 = nxx0.003`

     `n = 22.6`

 

So it will take about 23 months for Joanne to buy the truck.



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