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An employer wants to pay 450 dollars every 6 months to a deserving employee forever. The company has $A to fund the award and can earn j2= 7%(interest compounded semi-annually). If the first award is to be paid out 3 months from now, what is A?

i = 0.07/2 = 0.035

-So I've tried A = 450/0.035 and I didn't get the right answer

-I've tried A = 450 + 450/0.035 and that's not correct

-I've even tried (1.035)^-1*450/0.035

-I've also tried mixing the formulas but I still don't get the correct result and there are no examples or similar methods I could find in my textbook. I'm not sure how to approach this question at all.

Zain
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1 Answers1

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$$a_3 \equiv \frac{450}{0.035}$$ Is the amount that you need in the account in three months time after earning 3 months interest and paying your first \$450

The six month growth factor is 1.035

so the three month growth factor is $\sqrt {1.035}$

So your initial amount $A$ is the solution to ... $$ A\sqrt {1.035} -450=a_3$$

WW1
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