GMAT Quant : Simple & Compound Interest

Concept: Finding the principal based on interest received.

The question given below is a problem solving question in Simple and Compound Interest.

Question: 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?

  1. $ 5500
  2. $ 11000
  3. $ 22000
  4. $ 2750
  5. $ 44000

Explanatory Answer

Video explanation will be added soon

Concept 1: Simple and compound interest for the first year is the same. So, the difference in interest earned between simple and compound interest is because Shawn earned interest on first year’s interest in the second year when investing in compound interest.

Shawn received an extra amount of ($605 - $550) $55 on his compound interest bond.

The extra interest earned on the compound interest bond is the interest earned in year 2 on first year’s interest = $ 55

Concept 2: Simple interest earns the same interest year on year.
Simple interest for 2 years is $550.
Simple interest for the first year = \\frac{550}{2}) = $275.
For the first year simple and compound interest earn the same interest.
Therefore, compound interest for first year = $275.
$55 is the interest earned during the second year on $275.
Therefore, the rate of interest = \\frac{55}{275}) * 100 = 20% p.a.

When investing in simple interest, 20% interest means that each year Shawn receives 20% of the original principal he invested in bonds as interest.

If 20% of his investment in bonds = $275, then his total investment in each of the bonds = \\frac{275}{20}) * 100 = $ 1375

He has invested equal sums in both the bonds, his total savings before investing = 2 * 1375 = $ 2750.

Choice D is the correct answer.

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