pre calc question

Question

A savings account pays interest at a annual percentage rate (APR) of 2.6%, compounded weekly. Find the annual percentage yield (APY) for this account.

Give your answer as a percentage, rounded to three decimal places.

Answer: APY =  %

Answer 1

To find the annual percentage yield (APY) for a savings account, we use the formula:

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

where r is the annual percentage rate (APR) and n is the number of times the interest is compounded in a year.

In this case, the APR is 2.6% and the interest is compounded weekly, so n = 52 (52 weeks in a year).

We can plug in the values into the formula:

APY = (1 + 0.026/52)^52 - 1

Simplifying this expression, we get:

APY = 0.02636 or 2.636%



Therefore, the annual percentage yield (APY) for this savings account is 2.636%, rounded to three decimal places.