Question

Steven wants to start an IRA that will have $375,263 in it when he retires in 30 years. How much should he invest semiannually in his IRA to do this if the interest is 5.5% compounded semiannually? Assume an Annuity Due. Round to the nearest cent.

Answer 1

Hi there
The formula of the future value of annuity due is
Fv=pmt [(1+r/k)^(kn)-1)÷(r/k)]×(1+r/k)
Fv future value 375263
PMT semiannual payment?
R interest rate 0.055
K compounded semiannual 2
N time 30 years
We need to solve the formula for PMT

PMT=Fv÷[(1+r/k)^(kn)-1)÷(r/k)]×(1+r/k)
PMT=375,263÷((((1+0.055÷2)^(2
×30)−1)÷(0.055÷2))×(1+0.055÷2))
=2,454.28....answer

Good luck!