Question

Suppose you invest $ 800 in an account paying 6 % interest per year.   a. What is the balance in the account after 2 ​years? How much of this balance corresponds to​ "interest on​ interest"? b. What is the balance in the account after 30 ​years? How much of this balance corresponds to​ "interest on​ interest"? a. What is the balance in the account after 2 ​years? The balance in the account after 2 years is ​$ nothing. ​ (Round to the nearest​ cent.) How much of this balance corresponds to​ "interest on​ interest"? The amount that corresponds to interest on interest is ​$ nothing. ​ (Round to the nearest​ cent.) b. What is the balance in the account after 30 ​years? The balance in the account after 30 years is ​$ nothing. ​(Round to the nearest​ cent.) How much of this balance corresponds to​ "interest on​ interest"? The amount that corresponds to interest on interest is ​$ nothing. ​(Round to the nearest​ cent.)

Answer 1

We know that Future value for single cashflow is given by

FV= Amount*(1+ interest )^n

where n is the number of years.

A) Balance in the account after 2 years

Future value= 800*(1+0.08)^2= $933.12

Balance corresponds to​ "interest on​ interest" :

FIrst we have to find the interest amount by using the Simple Interest formula I= P*R*T= > I=800*0.08*2= 128.00

Interest on Interest= Future value- initial value amount- interest amount

Hence IOI= 933.12-800-128= $5.12

B)

Balance in the account after 30 years

Future value= 800*(1+0.08)^30= $8050.13

Balance corresponds to​ "interest on​ interest" :

FIrst we have to find the interest amount by using the Simple Interest formula I= P*R*T= > I=800*0.08*30= 1920

Interest on Interest= Future value- initial value amount- interest amount

Hence IOI=8050.13-800-1920 = $5330.13