Question

Alex wants to start an IRA that will have $1,250,675 in it when he retires in 30 years. How much should he invest semiannually in his IRA to do this if the interest is 4.5% compounded semiannually? Assume an Annuity Due. Round to the nearest cent.

Answer 1

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 1250675
PMT semiannual payment?
R interest rate 0.045
K compounded semiannual 2
N time 30 years
Solve the formula for PMT
PMT=Fv÷ [(1+r/k)^(kn)-1)÷(r/k)]×(1+r/k) Plug in the formula
PMT=1,250,675÷((((1+0.045
÷2)^(2×30)−1)÷(0.045÷2))×(1+0.045÷2))
=9,828.44...Answer

Hope it helps!

Answer 2

Answer:

$9828.44

Step-by-step explanation:

The semi annual payment is such that the future value of the annuity due is equal to the desired amount when he retires.

The formula to calculate future value of an annuity due periodic payment of M  for time period T for given periodic return r,

A=$\frac{M(1+r)^{T+1}-(1+r)}{r}$

in this question there are 30*2= 60 payments and the semi annual rate= 4.5/2= 2.25%

putting values we get

1250675= $\frac{M(1+2.25%)^{60+1}-(1+2.25%)}{2.25%}$

on solving we get M= $9828.44

Alex needs to invest $9828.44 semiannually in his IRA