Suppose United Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year. What is the effective annual rate on the loan?

The effective annual rate on loan would be 8.24%

Explanation:

Formula for Effective annual rate (EAR) -

(1 + APR / Number of compounding periods in a year) ^ (Number of compounding periods in a year) - 1

where, the APR IS 8%,

Number of compounding periods - 4 quarters

So now putting these values in the formula -

(1+8% / 4) ^4 - 1

= (1 + 2%) ^4 - 1

= (1 +.02) ^4 - 1

= (1.02) ^4 - 1

= 1.08243216 - 1

=.08243216

Now multiplying this by 100 to make it in percentage

= 8.24% (approximately)