Question

Assume you have a brand new baby today. You plan to make 18 $1,000 annual deposits in her college savings account, starting on her 1st birthday (that is, at the end of her first year of existence) and concluding on her 18th birthday. If the account earns 9% per year, compounded annually, what will be the balance in her account after her 18th birthday?

Answer 1

After her 18th birthday the balance will be $41,301

Step-by-step explanation:

Balance right after the 18th birthday is calculated using the formula for future value of annuity

FV =
`PMT * ((1+i)^(n)-1)/(i)`

Annual payment PMT = 1,000

Interest rate i = 0.09

Deposits are made for 18 years: n = 18

The balance in her account will then be:

FV = 1,000 * ( 1.09^18 - 1 ) / 0.09

= $41,301