Consider the effective annual rate of interest to be $18%$ for this question.
A man invests in a structured note and will receive bonus payouts of $300$, $400$, $500$ at the beginning of the first,third and fifth year respectively.
(i) At which point in time will a single payout of $1200$ be equivalent to these bonus payouts? Give your answer to the nearest $o.1$ year.
(ii) What is the future value, to the nearest dollar, of these payouts at the end of the tenth year?
Solution
(i)
$1200(1.18)^t=300+400(1.18)^3+500(1.18)^5$
Solving for $t$, $t=4.9$
For (ii), I do not understand how I should proceed
For (ii), add up the future values until $t=10$ for each payout to get $$300(1.18)^9+400(1.18)^7+500(1.18)^5$$ Alternatively, using (i), you might compute the future value of $1200(1.18)^{4.9}$ over the remaining time until $t=10$: $$1200(1.18)^{4.9}(1.18)^{10-4.9}$$