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lukranit [14]
4 years ago
9

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.
Business
1 answer:
Wittaler [7]4 years ago
8 0
<span>25 years: No Payment, but total is 250000
6 months earlier. Payment of "P". It's value 1/2 year later is P(1+0.03)
6 months earlier. Payment of "P". It's value 1 year later is P(1+0.03)^2
6 months earlier. Payment of "P". It's value 1½ years later is P(1+0.03)^3
6 months earlier. Payment of "P". It's value 2 years later is P(1+0.03)^4

</span><span>We need to recognize these patterns. Similarly, we can identify the accumulated value of all 50 payments of "P". Starting from the last payment normally is most clear.
</span>
<span>P(1.03) + P(1.03)^2 + P(1.03)^3 + ... + P(1.03)^50
 That needs to make sense. After that, it's an algebra problem.
 P[(1.03) + (1.03)^2 + (1.03)^3 + ... + (1.03)^50]
</span>
P(<span><span>1.03−<span>1.03^51)/(</span></span><span>1−1.03) </span></span>= <span>250000</span>
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