The question given below is a problem solving question in Simple and Compound Interest.
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?
- $ 5500
- $ 11000
- $ 22000
- $ 2750
- $ 44000
The correct choice is (D) and the correct answer is $ 2750
Shawn received an extra amount of ($605 - $550) $55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year.
The extra interest earned on the compound interest bond = $ 55
The interest for the first year = $
= $ 275
Therefore, the rate of interest =
= 20% p.a.
20% interest means that Shawn received 20% of the amount he invested in the bonds as interest
If 20% of his investment in one of the bonds = $275, then his total investment in each of the bonds =
= $ 1375
As he invested equal sums in both the bonds, his total savings before investing = 2*1375 = $ 2750.