Question

Andrew and Emma Garfield invested $7,900 in a savings account paying 4% annual interest when their daughter, Angela, was born. They also deposited $1,200 on each of her birthdays until she was 17 (including her 17th birthday). How much was in the savings account on her 16th birthday (after the last deposit)?

Answer 1

$44,440.96

Step-by-step explanation:

We must find the future value of the initial $7,900 deposit and the annuity (17 deposits of $1,200 each)

• future value of the initial deposit = present value x (1 + interest rate)ⁿ = $7,900 x 1.04¹⁸ = $16,003.95
• future value of the annuity = Payment x ([1 + interest rate]ⁿ - 1) / interest rate = $1,200 x (1.04¹⁷ - 1) / 0.04 = $28,437.01

total amount on Angela's savings account = $16,003.95 + $28,437.01 = $44,440.96