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

Answer:

See explanation

Step-by-step 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

$n = \frac{Log(1.31)}{Log(1 + 5\%)}$

Express 5% as decimal

$n = \frac{Log(1.31)}{Log(1 + 0.05)}$

$n = \frac{Log(1.31)}{Log(1.05)}$

$n = \frac{0.1173}{0.0212}$

$n \approx 6$

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

Use the above explanation to answer your question