Question

Siân is saving for a car which costs 11 800 AUD. Find how many years it will take for the value of the investment to reach this value. Round to the nearest year.

Answer 1

See explanation

Explanation:

The question is incomplete as the invested amount and the interest rate are not given. However, I will give a general method of solving it.

Assume that:

`r = 5\%` --- interest rate

`PV =9000` --- Present value or invested amount

To calculate time (in years), we make use of the following formula of future value

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

Where

`FV = 11800`

So:

`11800 = 9000( 1 + 5\%)^n`

Divide both sides by 9000

`1.31 = ( 1 + 5\%)^n`

Take logarithm of both sides

`Log(1.31) = Log(1 + 5\%)^n`

Apply law of logarithm

`Log(1.31) = nLog(1 + 5\%)`

Make n the subject

`n = (Log(1.31))/(Log(1 + 5\%))`

Express 5% as decimal

`n = (Log(1.31))/(Log(1 + 0.05))`

`n = (Log(1.31))/(Log(1.05))`

`n = (0.1173)/(0.0212)`

`n \approx 6`

The time to reach the future value is approximately 6 years.

Use the above explanation to answer your question