Question

Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $250.00 at the end of each quarter and then pay off the principal amount at the end of the year. What is the effective annual rate on the loan

Answer 1

Answer:

10.38%

Explanation:

From the question above a bank offers to lend an amount of $10,000 for a period of 1 year

The bank expects an interest of $250 to be paid every 4 months

= $250×4

= $1,000

Total amount of interest= $1,000

The first step is to calculate the nominal interest

= (1000/10,000)×100

= 0.1×100

= 10%

Therefore, the effective annual rate on the loan can be calculated as follows

= (1+r/m)^m-1

r = 10% , m = 4

= [1+(10/100)/4]^-1

=[ (1+0.1/4)^4]-1

= (1+0.025^4)-1

= (1.025^4)-1

= 1.1038-1

= 0.1038×100

= 10.38%

Hence the effective annual rate in the loan is 10.38%