Question

Ruben invested $1300 per year in an IRA each year for 6 years earning 14% compounded annually.

At the end of 6 years he ceased the IRA payments, but continued to invest his accumulated amount at 14% compounded annually for the next 8 years.

a) What was the value of his IRA at the end of 6 years?

Answer = $

b) What was the value of the investment at the end of the next 8 years?

Answer = $

Answer 1

a) Future value of IRA at the end of 6 years = (annual investment/annual interest rate)*[(1+annual interest rate)^{no. of years} - 1]

Future value of IRA at the end of 6 years = ($1,300/0.14)*[(1+0.14)⁶ - 1] = $9,285.7142857142857142857142857143*(1.14⁶ - 1) = $9,285.7142857142857142857142857143*(2.194972623936 - 1) = $9,285.7142857142857142857142857143*1.194972623936 = $11,096.17436512 or $11,096.17

the value of his IRA at the end of 6 years was $11,096.17.

b) Future value of the investment at the end of the next 8 years = present value*(1+annual interest rate)^{no. of years}

Future value of the investment at the end of the next 8 years = $11,096.17436512*(1+0.14)⁸ = $11,096.17436512*1.14⁸ = $11,096.17436512*2.8525864220672256 = $31,652.80

the value of the investment at the end of the next 8 years was $31,652.80.