Question

Stan wants to start an IRA that will have $250,000 in it when he retires in 25 years. How much should he invest semiannually in his IRA to do this if the interest is 6% compounded semiannually? Assume an Annuity Due. Round to the nearest cent

Answer 1

See the formula of the future value of annuity due through Google
Solve for PMT
PMT=250,000÷((((1+0.06÷2)^(2
×25)−1)÷(0.06÷2))×(1+0.06÷2))
=2,151.82

Answer 2

He sould invest $2,151.82

Explanation:

Data:

FV = $250,000

n = 25 years = 50 semesters

i = 6% annually / 2 semesters = 3% = 0.03

`PMT = (i*FV)/((1+i)^(n)-1)x(1)/((1+i))=(0.03*250,000)/((1+0.03)^(50)-1)x(1)/((1+0.03))=(7,500)/((1.03)^(50)-1)x(1)/((1.03))=(7,500)/(4.3839-1)x0.970873=(7,500)/(3.3839)x0.970873=2,216.38x0.970873=2,151.82`

Hope this helps!