Algebra Foundation Quiz #2 Question 3 [Spoiler]

GRE Quant Problem Solving
1

Blessing invests \$100 in a bank account earning 8% annual interest compounding quarterly.

  • Quantity A: The amount of interest Blessing earns on her \$100 investment after one year
  • Quantity B: 100(.02)^4

The answer is A (Quantity A is greater.), but I got C (The two quantities are equal.). I tried figuring out on my own why it’s A, but I keep getting the same answer unfortunately.

Here’s what I did to calculate Quantity A.

The formula for calculating the compound interest (without calculating the principle) is p(\frac{r}{100n})^{tn}. I tried plugging the above numbers in the formula.

The principle is p=100.
The interest rate % is r=8.
The number of compounding periods per year is n=4.
The number of years is t=1.

Quantity\ A
=100(\frac{8}{100 \times 4})^{1 \times 4}
=100(\frac{2}{100})^{4}
=100(0.02)^{4}

Since Quantity B is similarly 100(.02)^4, shouldn’t the answer be C? (I’m probably making some silly mistake somewhere.)

2

No, where’d you get this?

FV = P (1 + \frac rn)^{nt}

It should be clear that you can’t just get rid of the “1 + …” to get the “interest alone” because that’s not how binomial expansion works.

You’d be instead looking at something like:

CI = P (1 + \frac rn)^{nt} - P

1 Like