Question

Bianca has a choice between three savings accounts. Savings account A has an APR of 3.9998%, compounded semiannually; savings account B has an APR of 3.9742%, compounded monthly; and savings account C has an APR of 3.9886%, compounded quarterly. Bianca wants to choose the savings account with the highest APY. (5 points: Part I – 1 point; Part II – 1 point; Part III – 1 point; Part IV – 1 point; Part V – 1 point) Part I: If r is a savings account's APR and n is the number of compounding periods per year, what expression gives the savings account's APY?

Answer 1

APY = (1 +r/n)^n -1

Explanation:

Each period the principal is multiplied by 1 plus the periodic rate: 1 + r/n. For n periods in a year, the effective multiplier is (1 +r/n)^n. The value after this multiplication includes the principal, so to find the interest, we need to subtract the principal. The effective rate is ...

APY = (1 +r/n)^n -1

_____

You didn't ask, but the effective rates for the accounts shown are given in the attachment. The formula bar shows the formula used, and the highlighted cell shows the highest APY.

(I find a spreadsheet is a simple way to do repetitive calculations with minimal chance of error.)