# EAR vs quaterly compounding

Hi all,

I tried to calculate the loan payments for a 5 year loan of a total of 50k with an annual rate of 9% compounded quarterly using two methods:

1st→Calculating the EAR = 9.31%, then getting the annual payment = 12957.6 and then dividing by 4, so the quarterly payment is 3239.4

2nd→Introducing 20 periods in the BAII plus (5 years X 4 quarters) and a quarterly rate of 9/4 = 2.25%. that results in a quarterly payment of 3132.1

Why are the results different? Shouldn’t they be the same?

Thanks!

They shouldn’t be the same.

You lied to the calculator the first time: you told it that you were going to make principal payments once per year, when, in reality, you’re making principal payments four times per year. When you make the first quarterly payment you reduce the principal, so the interest is now a lower amount.

Try the problem 2 ways:

P/Y= 4, C/Y =4, I=9, N=20 Pv=50000 CPT PMT

P/Y=4, C/Y =1, I=9.30833, N=20, PV=50000 CPT PMT

Prepare to be amazed.

And never lie to your calculator. It will be your only friend during the exam.

Retry. They can’t be same.

Any difference in payment will be fractions of a penny.

(1 + 0.09/4)4 = 1.09308