Question

Karl opens a savings account with $2500. He deposits $1500 every year into the account that has a 0.75% interest rate, compounded monthly. If he doesn't withdraw any money, what will the account balance be in 10 years?

Answer 1

Total FV= $29,335.25

Step-by-step explanation:

First, we need to calculate the future value of the initial investment ($2,500) using the following formula:

FV= PV*(1 + i)^n

PV= $2,500

i= 0.0075

n=10*12= 120 months

FV= 2,500*(1.0075^120)

FV= $6,128.39

Now, the future value of the $1,500 annual deposit:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

We need to determine the effective annual rate:

Effective annual rate= (1.0075^12) - 1= 0.0938

FV= {1,500*[(1.0938^10) - 1]} / 0.0938

FV= $23,206.86

Total FV= $29,335.25