Question

You deposit $1,100 at the end of each year into an account paying 9.1 percent interest.

(a) How much money will you have in the account in 19 years?

(b) How much will you have if you make deposits for 38 years?

Answer 1

Answer a.

Annual deposit = $1,100
Interest rate = 9.10%
Period = 19 years

Accumulated sum = $1,100*1.091^18 + $1,100*1.091^17 + ... + $1,100*1.091 + $1,100
Accumulated sum = $1,100 * (1.091^19 - 1) / 0.091
Accumulated sum = $1,100 * 46.50583
Accumulated sum = $51,156.41

So, you will have $51,156.41 in your account after 19 years.

Answer b.

Annual deposit = $1,100
Interest rate = 9.10%
Period = 38 years

Accumulated sum = $1,100*1.091^37 + $1,100*1.091^36 + ... + $1,100*1.091 + $1,100
Accumulated sum = $1,100 * (1.091^38 - 1) / 0.091
Accumulated sum = $1,100 * 289.82574
Accumulated sum = $318,808.31

So, you will have $318,808.31 in your account after 38 years.