Question

Problem 5-20 Calculating the Number of Periods (L04) You expect to receive $31,000 at graduation in two years. You plan on investing it at 9.25 percent until you have $166,000. How long will you wait from now? (Do not round Intermediate calculations and round your answer to 2 decimal places, e.g. 32.16.) Period years

Answer 1

future value = present value * (1 + r)ⁿ

where r = rate of interest per year

n = number of years

$166,000 = $31,000 * (1 + 9.25%)ⁿ

1.0925ⁿ = (166,000 / 31,000)

n = log_1.0925(166,000 / 31,000)

n = 18.97 years

You will have to wait 18.97 years from graduation.

Number of years to wait from today = 18.97 + 2

Number of years to wait from today = 20.97

Answer 2

SOLUTION :

Let FV of $166000 be after n years from now on investing $31000 at 2 years from now.

So,

PV at year 2 = $31000 

FV at year n = $166000

Hence, (n - 2) years are required for the above to happen.

Interest rate = 9.25% = 0.0925

=> 1 + r = 1.0925

Therefore,

166000 = 31000 * 1.0925^(n - 2)

=> (1.0925)^(n-2) = 166000/31000 = 166/31

Taking log :

=> (n - 2) log(1.0925) = log(166/31)

=> n = log(166/31) / log(1.0925) + 2

=> n = no. of years needed from now = 20.97 years (ANSWER).