Question

You inherit $30,000. For 12 years, the money is invested in a mutual fund earning an annual rate of return of 6.4%. For the next 16 years, you make monthly contributions of $400 at the end of each month. If the account yields a 5.7% APR compounded monthly during that time, what is the account balance immediately following the final deposit?

Answer 1

$30,000 was invested for 12 years at annual rate of 6.4%.

Investment Value = A * ( 1 + i ) ^ n

i = Annual Int Rate = 6.4%

n = period = 12 Years

A = 30,000

Current Value of $30,000 =  30,000 * ( 1 + 6.4%)^ 12 = 63156. 90

Now 63156. 90 will be Invested for next 16 years  at annual rate of  5.7%

Future Value = A * ( 1 + i ) ^ n

Investment Value = A * ( 1 + i ) ^ n

i = Annual Int Rate = 5.7%

n = period = 16 Years

A = 63156. 90

Future Value of $ 63156. 90 after 16 years =  63156. 90 * ( 1 + 5.7%)^ 16 = 153327.69

Now Value of $ 400 monthly contribution after 16 Years =

P = Monthly Contribution = 400

i = Int Rate (Monthly) = 5.7% / 12 = 0.00475

n = periods = 16*12 = 192 Months'

Now Value of $ 400 monthly contribution =

= 1,24,962.29

the account balance immediately following the final deposit = Value of $ 400 monthly contribution after 16 Years + uture Value of $ 63156. 90 after 16 years = 1,24,962.29 +  153327.69 = 278289.9793

Ans : the account balance immediately following the final deposit  278289.9793