# On Ashley's 18th birthday, she receives a gift of \$10000, the accumulated amount of an investment her grandfather made for her when she was born.Determine the amount of the investment if the...

On Ashley's 18th birthday, she receives a gift of \$10000, the accumulated amount of an investment her grandfather made for her when she was born.

Determine the amount of the investment if the interest rate was 6.75% compounded: annually, semi-annually and monthly.

Posted on

Assume Ashley's grandfather invested an amount A when she was born. On her 18th birthday she receives \$10000.

The annual rate of interest on the amount invested is 6.75%.

This gives:

For compounding done annually

10000 = A*(1.0675)^18

=> A = `10000/1.0675^18`

=> A = \$ 3085.87

For compounding done semiannually

A = `10000/1.03375^36`

=> A= \$ 3027.2

For compounding done monthly

A = `10000/(1.005625)^216`

=> A = \$2977.21

The amount invested initially was \$ 3085.87 for annual compounding, \$3027.2 for semi-annual compounding and \$2977.21 for monthly compounding.