Question

As the winner of a competition you are entitled to $5,000 at the end of next year, with the amount growing at 5% p.a. for 10 years. Assuming the interest rate for valuing this prize is 10% p.a., its future value at the end of year 10 will be closest to:

Answer 1

First we need to find the cashflows for every year increasing at 5%. For example Year2=5000*(1+5%)=5250

Year4=Year3*(1+5%)=$5788.13

Now we need to find the compounding for each year at 10% interest rate and then sum it.

Please remeber the payments are made at the end of the year

Year1 value=5000*(1+10%)^9=$11789.74

Year4 value=5788.13*(1+10%)^6=$10254.02

Year10 value=$7756.64

Sum of the all years =$96,484.78 which is the future value

	Growing at 5% every year	Compounding
Year1	5000.00	11789.74
Year2	5250.00	11253.84
Year3	5512.50	10742.30
Year4	5788.13	10254.02
Year5	6077.53	9787.92
Year6	6381.41	9343.02
Year7	6700.48	8918.34
Year8	7035.50	8512.96
Year9	7387.28	8126.00
Year10	7756.64	7756.64
Future Value		96484.78	SUM