The given question is a GMAT 650 level problem solving question from the topic Simple Interest and Compound Interest. Concepts Tested: 1) In simple interest, interest earned is the same value year on year. 2) Further, interest earned is same for both Simple and compound interest for the first year. 3) Interest earned on first year's interest will get added in the second year, when interest is compounded annually.

Question 16: 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

@ INR

**Simple Interest:**

**Concept:**Simple interest earned is same value year on year.

Shawn received $550 as interest for 2 years.

Simple interest earned for first year =\\frac{\text{550}}{\text{2}}\\) = $275

The simple interest for second year is also $275.

**In Compound interest:**Shawn received $605 as interest for 2 years.

**Concept:**Interest earned is same for both simple and compound interest in the first year.

Compund interest earned for first year = $275.

Compund interest earned for second year = 605 − 275 = $330

Extra interest received from compound interest = $55.

Simple Interest | Compound Interest | |
---|---|---|

First year interest | $275 | $275 |

Second year interest | $275 | $330 |

Total interest | $550 | $605 |

**Concept:**In Compound interest, interest earned on first year's interest will get added in second year and contributes to the additional interest when invested in compound interest.

Compound interest for first year = $275.

Therefore, $55 is the interest earned during the second year on $275.

Therefore, the rate of interest = \\frac{\text{55}}{\text{275}}\\) × 100 = 20% p.a.

At 20% rate of interest, the simple interest earned for 1 year = $275

Simple interest = \\frac{\text{Principal × number of years × rate of interest}}{\text{100}}\\)

275 = \\frac{\text{P × 1 × 20}}{\text{100}}\\)

or P = $1375

Shawn had invested equal sums in both the bonds.

His total savings before investing = 2 × 1375 = $2750

**Total savings = $2750**

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