You want to buy a car, and a local bank will lend you $20,000. The loan will be fully amortized over 5 years (60 months), and th

Question

3 years ago

15

You want to buy a car, and a local bank will lend you $20,000. The loan will be fully amortized over 5 years (60 months), and th

e nominal interest rate will be 10% with interest paid monthly.
1. What will be the monthly loan payment?

2. What will be the loan's EAR?

Business

1 answer:

EastWind [94] · Answer 1 · 2022-03-31T14:28:42+03:00

Amortizing a loan P over n periods at i% interest / period, the payment per period is given by:
$A= P(i(1+i)^n)/((1+i)^n-1)$

In given situation,
P=20000
period=month
i=10%/12
n=5*12=60 months

A. monthly payment amount
$A= P(i(1+i)^n)/((1+i)^n-1)$
$= 20000(.1/12(1+.1/12)^60)/((1+.1/12)^60-1)$
$=424.98$ to the nearest cent

B. EAR (effective annual rate)
the APR is 10%, but compounded monthly.
So
EAR=(1+i/12)^12-1
=(1+0.1/12)^12-1
=0.104713
=10.4713% (effective annual rate)