Question

Fifteen years ago a couple purchased a house for $230,000.00 by paying a 20% down payment and financing the remaining balance with a 30-year mortgage at 4.7% compounded monthly.

(a) Find the monthly payment for this loan.

(b) Find the balance of the loan after 16 years and after 17 years?

(c) Find the total amount of interest paid by the couple during the 17th year.

Answer 1

(a)

Monthly payment for this loan

$       954.34

Working:

# 1

Present Value of annuity of 1

=

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

Where,

=

(1-(1+0.003917)^-360)/0.003917

i

4.7%/12

=

0.003917

=

192.803846

n

30*12

=

360

# 2

Purchase Price of House

a

2,30,000

Less:Down Payment

b=a*20%

46,000

Loan Amount

1,84,000

# 3

Monthly payment for this loan

=

Loan amount / Present Value of annuity of 1

=

1,84,000

/

192.8038

=

954.34

(b)

Loan Balance after;

16 Years

$ 1,17,307.00

17 Years

$ 1,11,239.24

Working:

Loan is the present value of monthly payment.

After 16 Years, Present Value of monthly Payment

=

$           954.34

*

122.9198

=

$ 1,17,307.00

Present Value of annuity of 1 for 14 Years

=

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

Where,

=

(1-(1+0.003917)^-168)/0.003917

i

4.7%/12

=

0.003917

=

122.9198

n

14*12

=

168

After 17 Years, Present Value of monthly Payment

=

$           954.34

*

116.5617

=

$ 1,11,239.24

Present Value of annuity of 1 for 14 Years

=

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

Where,

=

(1-(1+0.003917)^-156)/0.003917

i

4.7%/12

=

0.003917

=

116.561698

n

13*12

=

156

(c)

Total Interest paid during year 16

$       5,384.28

Working:

Total Payment during year 17

=

$           954.34

*

12

=

$    11,452.05

Reduction in Principal

=

$ 1,17,307.00

-

$ 1,11,239.24

=

$      6,067.77

Interest paid

$      5,384.28