Question

The owner of a small business borrowed $300,000 today (year 0) with an agreement to repay the loan with equal quarterly payments over a five year time period. If the interest rate is nominal 24% per year compounded quarterly, his loan payment each quarter is equal to:

A. $109,275

B. $71,220

C. $26,154

D. $19,938

Answer 1

C. $26,154

First of all we need to find effective rate of interest,

r= (1+i/m)ⁿ-1

where r is effective rate of interest

i= nominal interest rate

m= compounding periods in 1 year

n= total compounding periods

here, i= 24/100= 0.24

m=4

n=15

so, r= (1+0.24/4)¹⁵-1

r= 1.39655

So, quarterly payment will be (1.39655*300,000)/15= $26,154 Ans.