Question

Calculate the future value of

$ 10 000$

in

a.

Four

years at an interest rate of

5 %

per year.

b.

Eight

years at an interest rate of

5 %

per year.

c.

Four

years at an interest rate of

10 %

per year.

d. Why is the amount of interest earned in part

​(a​)

less than half the amount of interest earned in part

​(b​)?

Answer 1

A) Given

P=$10000

r=5%

N=4 years

So FV=P*(1+r)^N

FV=10000*(1+5%)^4=$12155.06

B)

P=$10000

r=5%

N=8 years

So FV=P*(1+r)^N

FV=10000*(1+5%)^8=$14774.55

C)

P=$10000

r=10%

N=4 years

So FV=P*(1+r)^N

FV=10000*(1+10%)^4=$21435.89

D)

Interest earn in part A = 12155.06-10000=$2155.06 Eq1

Half of interest earn in Part B= (14774.55-10000)/2=$2387.28 Eq2

From Equation 1 and 2 it is clear that half of interest earn in part B is greater than interest earn in part A. Because n part B are earning interest also on interest accumulated which is power of compounding so half of interest earn in part B is greater than interest earn in part A.