Question

You just found the house of your dreams. The price of the house is ​$500,000. You have been qualified to get a mortgage loan with AAA Bank. The mortgage loan is for 30 years at an annual interest rate of 36%.

Part​ (A):

How much are your monthly payments for the​ loan?

Part​ (B):

What is the balance of the mortgage loan after 2 ​year(s) of​ payments?

Part​ (C):

After 2 years of​ payments, you want to add extra money to the monthly payments so that you will be able to pay off the mortgage loan in 10

years. How much do you have to add to your previously computed monthly payments in order to accomplish​ this?

1. Components to arrive to the answer to part​ (A):

How many periods​ (the value of​ n) do we need to use in computing the monthly payments​ (PMT)? ______

2. What is the rate per period to use in solving the monthly payments for the mortgage​ loan?

____​%  ​(Round to two decimal places and enter them. Do not enter the​ % symbol. For​ example, if the answer is 2.43​ percent, then enter​ 2.43)

3. How much is the monthly payment for the mortgage​ loan?

​$____​(Round to two decimal places and make your your answer has two decimals. Do not enter​ and use commas to separate thousands. For example if the answer is​ $1,000.20 then enter​ 1,000.20)

4. Components to arrive to the answer to part​ (B):

To compute the balance of the mortgage loan after 2 ​year(s), what is the value of n​ (number of​ periods) to​ use?____periods

5. After 2 ​years, what is the balance of the mortgage​ loan?

​$________ ​(Round to two decimal places and make your your answer has two decimals. Do not enter​ $ and use commas to separate thousands. For example if the answer is​ $1,000.20 then enter​ 1,000.20)

6. Components to arrive to the answer to part​ (C):

These calculations are after you have made payments for 2 year(s). What is the value of n in the calculations of the new monthly​ payments?  

_______periods

7. How much are the new monthly payments​ (in order to pay off the loan in 10 ​years? ​$_______

8. After 2 years of​ payments, you want to add extra money to the monthly payments so that you will be able to pay off the mortgage loan in 10 years. How much do you have to add to your previously computed monthly payments in order to accomplish​ this?

​$____(Round to two decimal​ places.)

Answer 1

Solution :

Amount of loan = $500000

Mortgage period = 30 years means 12*30 = 360 months

Annual interest rate = 36%

Means monthly rate = 36% / 12 = 3% per month

(A)

Now let monthly payment of loan = X

500000 = X * PVAF(3% , 360)

X = 500000 ÷ 33.3325

X = $15000.36

Monthly payment = $15000.36

(B)

Now the present value of the loan paid in two years =

First compute the present value of emi of remaining 28 years

= 15000.36 * PVAF(3% , 28*12)

= 15000.36 * 33.3317

= $499987.69

Now remaining loan balance after 2 years of payment =

= $499987.69

(c) Now if we want to pay of the loan in 10 years installment =

499987.69 = X * PVAF(3% , 10*12)

X = 499987.69 ÷ 32.373

X = 15444.589

Now amount needs to added in the installment to pay off the loan = $15444.589 - $15000.36 = $444.23

(1) n = 30*12 = 360

(2) 36 ÷ 12 = 3

(3) $15000.36

(4) n = 28*12 = 336

(5) Balance of mortgage loan = $499987.69

(6) n = 10*12 = 120

(7) $15444.59

(8) $444.23