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Question 996751: Jason invested $5000 in a bank savings account which offered 4.75% p.a. simple interest that is paid every six months. At the end of the first year Jason discovered that he could obtain an interest rate of 4.5% p.a. compounded monthly. If he kept all the previous interest in his account, how much interest could he earn in the next 12 months using this interest rate?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! simple interest is paid on the original investment only.
it doesn't compound.
he invested 5000 at 4.75% per year simple interest that is paid every six months.
at the end of the first year his interest earned was .0475 * 5000 = 237.5
that was .0475 * 5000 / 2 = 118.75 for the first 6 months and the same amount for the second 6 months.
at the end of the year he had his original 5000 + 237.5 in interest for a total of 5237.5
he invests 5237.5 at 4.5% interest annually compounded monthly.
the monthly interests rate is .045/12 = .00375.
at the end of the second year he would have 5237.5 * 1.00375^12 = 5478.109834.
if he had kept the money in the simple interest account, he would have had 5000 + 2 * 237.5 = 5475.
he didn't make a lot more, but he did make more.
the difference becomes much greater the longer you keep the money invested.
for example:
30 years at 4.75% per year on 5000 yields simple interest of 7125.
30 years at 4.5% per year on 5000 compounded monthly yields interest of 14238.
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