Question

You just found the house of your dreams. The price of the house is ​$400,000. You have been qualified to get a mortagage 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 after2 ​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 15 years. How much do you have to add to your previously computed monthly payments in order to accomplish​ this?

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)?

____  

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)

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)

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

After 2 ​years, what is the balance of the mortagage​ 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)

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

How much are the new monthly payments​ (in order to pay off the loan in 15 ​years?

​$______

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 15 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:

Part A:

Price of the House / Loan amount = $400000

Annual interest rate = 36%

Therefore, monthly interest rate = 36/12 = 3%

Loan tenure = 30 years = 360 months

Equated Monthly Installment = P * r *[ (1+r)ⁿ / ((1+r)ⁿ - 1) ]

where,

P= Principal Loan Amount

r=  rate of interest calculated on monthly basis

n=  loan term / tenure / duration in number of months

Applying the values

EMI = $400000*3%* [ (1+3%)³⁶⁰ / ((1+3%)³⁶⁰ - 1]

= $12000 [ 41821.62 / 41820.62 ]

= $12000.29

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)?

Ans: 360 months

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

Ans: 3

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

Ans: $12000.29

Part B

Balance Amount = [P (1+r)ⁿ ] - [ (E / r) ((1+r)ⁿ - 1)]

P = $4,00,000

r = 3%

n = 2 years = 24 months

E= EMI = $12,000.29

Applying the values

Balance Amount after 2 years

= [ 400000 (1 + 3%)²⁴ ] - [ (12000.29 / 3%) (( 1+3%)²⁴ -1 ]

= 813117.64 - [400009.67 * 1.03279411]

= 813117.64 - 413127.63

= $3,99,990.01

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?

Ans: 24 months

After 2 ​years, what is the balance of the mortagage​ loan?

Ans: 3,99,990.01

Part C

Equated Monthly Installment = P * r *[ (1+r)ⁿ / ((1+r)ⁿ - 1) ]

P = Balance of loan at the end of 2 years = $3,99,990.01

r = 3%

n = 15 years = 180 months

EMI = 399990.01 * 3% * [ (1+3%)¹⁸⁰ / (1+3%)¹⁸⁰ -1 ]

= 11990.7006 * [204.50336 / 203.50336]

  = $12058.67

Additional amount to be added to EMI to repay the loan in 15 years = EMI under Part C - EMI under Part A

= 12058.67 - 12000.29

= $58.38

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?

Ans: 180 months

How much are the new monthly payments​ in order to pay off the loan in 15 ​years?

Ans: $12058.67

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

Ans: $58.38