Question

New parents wish to save for their newborn's education and wish to have $59,000 at the end of 19 years. How much should the parents place at the end of each year into a savings account that earns an annual rate of 5.7% compounded annually? (Round your answers to two decimal places.)
$  

How much interest would they earn over the life of the account?
$  

Determine the value of the fund after 9 years

$

Answer 1

Answer a.

Desired sum after 19 years = $59,000
Annual interest rate = 5.70%

Let annual saving be $x

$59,000 = $x*1.057^18 + $x*1.057^17 + ... + $x*1.057 + $x
$59,000 = $x * (1.057^19 - 1) / 0.057
$59,000 = $x * 32.75405
$x = $1,801.30

Annual saving = $1,801.30

Answer b.

Total saving = 19 * $1,801.30
Total saving = $34,224.70

Interest earned = $59,000 - $34,224.70
Interest earned = $24,775.30

Answer c.

Value of fund after 9 years = $1,801.30*1.057^8 + $1,801.30*1.057^7 + ... + $1,801.30*1.057 + $1,801.30
Value of fund after 9 years = $1,801.30 * (1.057^9 - 1) / 0.057
Value of fund after 9 years = $1,801.30 * 11.34963
Value of fund after 9 years = $20,444.09