Question

Consider an amortizing loan. The amount borrowed initially is $21618, the interest rate is 5% APR, and the loan is to be repaid in equal monthly payments over 17 years. As we know, while each monthly payment will be the same, the amounts of interest and principle paid will change from payment to payment. How much of the very first payment is interest?

Answer 1

$ 90.08

Working:

Step-1:Monthly Payment Calculation

Monhly Payment

=

Loan Amount/Cumulative discount factor

=

$ 21,618

/

137.199

=

$ 157.57

Working:

Cumulative discount factor

=

(1-(1+i)^-n)/i

Where,

=

(1-(1+0.00417)^-204)/0.00417

i

=

5%/12

=

0.00417

=

137.199

n

=

17*12

=

204

Step-2:Repayment schedule of first month

Month

Beginning Loan balance

Interest for the month

Monthly Payment

Principal Repayment

Ending Loan Balance

a

b=a*5%*1/12

c

d=c-b

a-d

1

$ 21,618.00

$     90.08

$   157.57

$       67.49

$    21,550.51