ira retirement account

Question

Ruben invested $1400 per year in an IRA each year for 8 years earning 10% compounded annually.
At the end of 8 years he ceased the IRA payments, but continued to invest his accumulated amount at 10% compounded annually for the next 9 years.
a) What was the value of his IRA at the end of 8 years?b) What was the value of the investment at the end of the next 9 years?

 

show your work

Answer 1

The formula for the Future Value of an annuity is

Future Value = PMT [((1 + r)ⁿ - 1) / r] = $1400 [((1 + .1)⁸ - 1) /.1] = $16010.24

a. So Ruben would have $16010.24 at the end of 8 years.

 

b. at the end of the next years the investment would be worth

 

Future Value = Present Value * (1+r)ⁿ =  Present Value * (1.1)⁹ = $16010.24 * 2.357948 = $37,751.31

 

Ruben would have $37,751.31 at the end of 9 more years

Answer 2

For the first 8 years, use the ordinary annuity formula to compute the ending amount accumulated under the conditions you have stated.

Then use the compounding formula A(t) = A(0)(1.10)^t where A(0) is the above annuity cumulative value, and t=9.