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.
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%.
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.