Question

the kelowna go-kart club has decided to build a clubhouse five years from now. it must accumulate $50000 by the end of five years by setting aside a uniform amount from its dues at the end of each year. if the imterest rate is 10 percent, how much must be set aside each year?

Answer 1

Sol.

Future Value: $50000

Period: 5 Years

Interest Rate: 10%

We required to calculate present value of $50000 using the formula which is;

And the Present Value of series of payment is;

As we don’t know present value of each year investment hence we assume that $50000 ÷ 5 = $10000 each year is future value.

By using below formula we will calculate present value of year.

PV=[C1/(1+R)^1 + C2/(1+R)^2 + C3/(1+R)^3 + C4/(1+R)^4 + C5/(1+R)^5]

PV=[10000/(1+0.10)^1 + 10000/(1+0.10)^2 + 10000/(1+0.10)^3 + 10000/(1+0.10)^4 + 10000/(1+0.10)^5]

PV=[9090.90909 + 8264.46281 + 7513.14801 + 6830.13455 + 6209.21323]

Year	Present Value or Per Year Investment @10% for 5 years to accumulate $50000
1	$9090.909
2	$8264.463
3	$7513.148
4	$6830.135
5	$6209.213
Total	$37907.87

Note: Also there is another way to solve which is discounted way and the formula whic is;

​PV=FV×(1+i)−n

where:

PV=Present value (original amount of money)

FV=Future value

i=Interest rate per period

n=Number of periods​