Question

Find a suitable home for you and your family on a real estate website (Zillow, Trulia etc.) and provide me with a link. Round the home price to the nearest thousand dollars. Assume an interest rate of 3% and select a length of a mortgage (typically 15 or 30 years). Use this information to answer the following:

1. What is the monthly payment?

2. If you are 5 years into the mortgage, what is the remaining balance (show your work)?

3. What happens to the monthly payment if you get an interest rate that is 1 percentage point higher (i.e. 3%→4%)?

Answer 1

I cannot find the home for you and your family on a real estate website (Zillow, Trulia etc.) and provide with a link, but I can help you wth the calculations.

Assuming that the Price of the home you have selected is $ 180,000, and the tenure is assumed as 20 years for the below calculations.

Given that Interest rate = 3%

Solution a:

The Monthly Payment can be found using the below formula:

where P is the Loan Amount = $ 180,000

r is the Interest rate per period = 3%/12 = 0.0025

n is the number of periods = 20 * 12 = 240

Upon subctituting, we get,

EMI = 998.2757

Hence, Monthly Payment = 998.2757

Solution b:

If you are 5 years into the mortgage, what is the remaining balance?

This can be found using the Difference between the Future Value of the Loan and Future Value of the Payments made for the given period

Remaining balance :

FV = PV * (1+r)ⁿ

Here Annuity refers to the monthly Payments

PV = 180000

r = 0.0025

n=60 (5 years)

P = 998.2757

Upon substituting and solving, we get,

FV of Loan = 209091.02

FV of Payments = 64535.24

Remaining Balance = 209091.02 - 64535.24

Remaining Balance = 144,555.78

Solution c:

Interest rate is increased by 1 %

Interest rate = 4%

Interest rate per period = 4% / 12 = 0.0033

The Monthly Payment can be found using the below formula:

where P is the Loan Amount = $ 180,000

r is the Interest rate per period = 0.0033

n is the number of periods = 20 * 12 = 240

Upon subctituting and solving, we get,

EMI = 1090.76

Hence, the monthly payment in this case increased to 1090.76