Question

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%.

Answer 1

acc. 2 b

Explanation:

Answer 2

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

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%