Problem Solving

Hi M7MBA,

We're told that $1000 is placed into account X, yielding 10% interest compounded annually and $1000 is placed into account Y using 10% simple annual interest. We're asked how much more money will be in account X than in account Y at the end of 5 years. This question requires a certain amount of basic math, but the answer choices are 'spread out' enough that you don't have to calculate every step to get the correct answer.

To start, we're have to use two formulas:
Simple Interest = (Principal)(1 + RT) where R is the annual interest rate and T is the number of years
Compound Interest = (Principal)(1 + R)^T where R is the annual interest rate and T is the number of years

The $1000 invested at 10% simple interest would be worth ($1000)(1 + (.1)(5)) = $1500 at the end of 5 years - meaning that $500 of interest is generated.

For the $1000 invested at 10% compound interest, I'm going to do the calculations one year at a time:
Year 1: $1000(1.1) = $1100 .... account gains $100 in interest
Year 2: $1100(1.1) = $1210 .... account gains $110 in interest
Year 3: $1210(1.1) = $1331 .... account gains $121 in interest

At this point, you might notice that the interest gained in Year 3 was just a little MORE than $10 greater than the interest that was gained in Year 2. This pattern will continue on (with the difference in interest gained increasing slightly in Year 4 and Year 5). Thus, the total for the 5 years will be a little greater than....

Total interest > 100 + 110 + 120 + 130 + 140
Total interest > 600

Thus, the difference in the two totals will be a BIT GREATER than 600 - 500 = a BIT GREATER than $100. There's only one answer that fits...

Final Answer: C

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