Which account has the highest annual interest rate? A. Account 1: Interest is compounded annually at a rate of 3.28%. B. Account 2: Interest is compounded monthly at a rate of 3.25%. C. Account 3: Interest is compounded weekly at a rate of 3.10%. D. Account 4: Interest is compounded daily at a rate of 3.15%. E. Account 5: Interest is compounded quarterly at a rate of 3.25%.

Question

Mathematics

Randy Adkins

4 October, 08:05

Which account has the highest annual interest rate? A. Account 1: Interest is compounded annually at a rate of 3.28%. B. Account 2: Interest is compounded monthly at a rate of 3.25%. C. Account 3: Interest is compounded weekly at a rate of 3.10%. D. Account 4: Interest is compounded daily at a rate of 3.15%. E. Account 5: Interest is compounded quarterly at a rate of 3.25%.

+4

Answers (1)

Know the Answer?

Nash Watson · Answer 1

The highest annual interest rate is B. Account 2: Interest is compounded monthly at a rate of 3.25%

Step-by-step explanation:

Let's recall that the compounded interest formula is:

FV = P * (1 + r/n) ⁿ

where FV is the Future Value, P is the principal or initial deposit, r is the interest rate and n the number of times interest is applied per time period.

Now, let's assume we deposit $ 100 in each account. These will be the balances after 12 months (rounded to the next cent):

Account 1 = 100 * (1 + 0.0328) ¹ = 103.28 Account 2 = 100 * [1 + (0.0325/12) ]¹² = 103.30 Account 3 = 100 * [1 + (0.031/52) ]⁵² = 103.15 Account 4 = 100 * [1 + (0.0315/360) ]³⁶⁰ = 103.20 Account 5 = 100 * [1 + (0.0325/4) ]⁴ = 103.29

The highest annual interest rate is B. Account 2: Interest is compounded monthly at a rate of 3.25%