Question

Suppose you invest $2,500 in a fund earning 15% simple interest. Further suppose that you have the option at any time of closing this account and opening an account earning compound interest at an annual effective interest rate of 9%. At what instant should you do so in order to maximize your accumulation at the end of five years?(Round your answer to two decimal places.)

---- years

How about if you wish to maximize the accumulation at the end of ten years? (Round your answer to two decimal places.)

----- years

Answer 1

year	prinicipal	interest	cumulative investment
1	2500	375	2875
2	2500	375	3250
3	2500	375	3625
4	2500	375	4000
5	2500	375	4375

amount invested	$ 2,500.00
simple interst rate	15%
interst earned at simple interst rate(2500*15%)	$     375.00
compound interst rate	9%
prinicipal required to earn $375 at compund interst rate is (375/9%)	$ 4,166.67
to maximize income, convert from simple interest to compound interest when the sum of prinicipal & interst reaches at $4166.67
Cumulative amount upto 4 years is	$40,000
amount required during 4 th year is (4166.67-4000)	166.67
time required to return $166.67 is (166.67/375)*365	162.22547
we can switch from simple interst to compoound interest at 4 years and 162 days or 4 Years 5.33 months
A. To maximize accumulation at the end of 5 years, you should convert at 4 Years & 162 Days or 4 Years 5.33 months
B. To maximize accumulation at the end of 10 years, you should convert at 4 Years & 162 Daysor 4 Years 5.33 months
Answer for both the questions is same