Question

Bank pays 8.3% total interest on your savings account for the year. Interest is paid on a daily frequency. What is the APR for this account?

Answer 1

We have following formula to calculate annual percentage rate (APR)

Effective annual rate (EAR) = (1 + APR/m) ^m – 1

Where,

Bank’s Effective annual rate (EAR) =8.3% per year

Where, nominal annual interest rate annual percentage rate (APR) =?

Number of compounding per year, m = 365 (daily compounding, where number of days in a year is 365)

Therefore

8.3%= (1 + APR/365) ^365 - 1

Or 8.5% + 1 = (1 + APR/365) ^365

Or (1.083) ^ (1/365) = (1 + APR/365)

Or 1.000218476 = (1 + APR/365)

Or APR = (1.000218476 -1) *365

Or APR = 0.000218476 *365 = 0.079743678 or 7.97%

Therefore the APR for this account is 7.97%.