Larry wants to start an IRA that will have $730,000 in it when he retires in 30 years. How muchshould he invest semiannually in his IRA to do this if the interest is 9% compoundedsemiannually?
Answers
Given :- Larry wants to start an IRA that will have $730,000 in it when he retires in 30 years. How much should he invest semiannually in his IRA to do this if the interest is 9% compounded semi annually ?
Answer :-
we know that, when rate is compounded semi annually,
- Time = Double .
- Rate = Half .
so,
- FV = $730,000 .
- Rate = 9/2 = 4.5% annually = 4.5/100 = 0.045 = i
- Time = 30 * 2 = 60 years .
- PMT = ?
we know that,
- FV = PMT[{(1 + i)^n - 1}/ i]
putting all values we get,
→ 730000 = PMT[{(1 + 0.045)⁶⁰ - 1}/0.045]
→ 730000 = PMT[{(1.045)⁶⁰ - 1}/0.045]
→ 730000 = PMT[(14.03 - 1)/0.045]
→ 730000 = PMT(13.03/0.045)
→ PMT = (730000 * 0.045)/13.03
→ PMT ≈ $2521.61 (Ans.)
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