# GMAT Simple Interest & Compound Interest Q16

#### GMAT Quant Questions | Word Problem

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?

1. $5500 2.$ 11000
3. $22000 4.$ 2750
5. $44000 ## Get to Q51 in GMAT Quant #### Online GMAT Course From INR 3000 ### Video Explanation ## GMAT Live Online Classes #### Starts Sun, June 18, 2023 ### Explanatory Answer | GMAT Simple and compound interest #### Step 1 of solving this Question: Compute interest for each year for both simple and compound interest 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. #### Interest for each year Simple Interest Compound Interest First year interest $275$275 Second year interest $275$330 Total interest $550$605 #### Step 2 of solving this GMAT Question: Find the rate of interest 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. #### Step 3 of solving this GMAT Question: Compute the principal invested 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 #### Choice D is the correct answer. #### GMAT Online CourseTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GMAT Live Online Classes Next Batch June 18, 2023 ## Additional Practice Questions in Ratio Proportion, Mixtures, Percents, Fractions, Profits, and Interest ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 95000 48484
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