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What is APR and EAR ?


APR (Annual Percentage Rate):
 It is an annual percentage rate charged on mortgage, credit card etc. or earned on investment. It is an annual cost of borrowing the funds. It is a nominal rate or quoted rate that mentioned on a borrowing contract. It is lower than the EAR but higher than the interest rate (current rate of borrowing the amount). APR includes all the fees related to borrowing the funds.

EAR (Effective Annual Rate):
It is a compound interest rate that charged on borrowing fund or earned on investment. It is higher than APR. It is an amount what you actually pay or receive. As more and more compounding the interest rate the more you will get the EAR.

Difference between EAR and APR:
·         EAR is a rate what you really pay or receive while APR is a cost of borrowing the amount.
·         EAR includes compounding interest while APR is based on simple interest.
·         EAR is used to calculate the frequently compounded interest like credit card while APR is used to calculate the loan interest.

Formula:
EAR = (1+ i / n) n - 1
APR = n [(1 + EAR) 1 /n – 1]
Where,
i = interest rate
n = number of payments in one year

Example: Mr. Mehta wants to purchase a house so he takes a loan of Rs.45, 00, 000 from bank for 5 years. Bank charges interest @ 9.12% compounded monthly Find out the EAR of the loan and total amount paid at the end of 5th year.
Solution:  EAR = (1 + i / n) n – 1
= (1 + 0.0912 / 12) 12 – 1
= (1.0076) 12 – 1
= 1.095 – 1
= 0.095 or
= 9.5%

Example: Mr. Sharma wants to open a saving account in a bank. So, he has collected information regarding the interest rate offered by different banks on a saving account. The information is:
·         Bank P offers interest @ 8.9% compounded semi- annually on saving account.
·         Bank Q offers 10% interest annually.
·         Bank K offers 9% interest compounded daily on saving account.
Find out which gives higher interest on saving account?
Solution: EAR = (1 + i / n) n – 1
Bank P: Offers 8.9% compounded semi-annually and the EAR is
= (1 + 0.089 / 2) 2 – 1
= (1.0445) 2 – 1
= 1.0909 – 1
= 0.0909 or
= 9.09%
Bank Q offers 10% interest annually and the EAR is 10% interest annually. Because this is the annual interest rate not include any compounding.
Bank K offers 9% compounded daily interest and the EAR is:
= (1 + 0.09 / 365) 365 – 1
= (1.00024658) 365 – 1
= 1.094164 – 1
= 0.094164 or
= 9.41%
Bank Q offers high interest rate i.e. 10% in comparison to bank P and K.

Example: Find out the APR if the loan amount is Rs.78, 000 and the EAR of the loan is 7.2%. The loan amount paid in monthly.
Solution: APR = n [(1 + EAR) 1 /n – 1]
= 12 [(1 + 0.072) 1 /12 – 1]
= 12 [1.00578735 – 1]
= 12 * 0.00578735
= 0.06944 or
= 6.94%

Example: Find out if the borrower paid semi-annually interest @10% EAR to the lender then what percentage of APR received by lender?
Solution: APR =n [(1 + EAR) 1 /n – 1]
= 2 [(1 + 0.12) 1 /2 – 1]
= 2 [1.05830052 – 1]
= 2 * 0.05830052
= 0.1166 or
= 11.66%


 



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