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.
$$a_3 \equiv \frac{450}{0.035}$$ 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 ... $$ A\sqrt {1.035} -450=a_3$$