Question

Find a place to live in your preferred location.

a. Find a house available for purchase that is at least two bedrooms. Calculate a monthly payment associated with a 30-year fixed mortgage assuming you can make no down payment on this house. (use interest rate of 3.435% and house price of $244,900)

b. Calculate how long it would take you to save a $10,000 down payment for your house if you can invest 2% of your monthly income(monthly income is $3,995.01) into an account that earns 4% compounded monthly.

c. Calculate a new monthly payment for a 30-year fixed mortgage with the $10,000 down payment. How much did you save in interest for having the down payment?

d. Find an apartment available for rent, assuming you have no roommates. Calculate how much you will pay in rent over the course of the 30-year mortgage for the house if rent costs remain fixed. (use $785 as fixed apartment monthly rent)

PLEASE SHOW WORK

Answer 1

Question. a

Monthly Interest Rate = 3.435%/12 = 0.286%

Monthly Mortgage Payment = [P* R*(1+R)^N]/[(1+R)^N-1]

= [244990*0.286%*(1+0.286%)^360]/[(1+0.286%)^360-1]

= $ 1093.29

Question No. b

Monthly Investment = 3995.01 * 2% = $ 79.90

Rate of Return = 4%

Time Period required for $ 10,000

10,000 = 79.90 * FVAF (4%/12, n periods)

FVAF (4%/12, n periods) = 10,000/79.90 = 125.156

From Future Value Annuity Table , n = 105 Months

Question No. C

Total Interest Payment on Loan of $ 244990 = 1093.29*360 - 244990 = $ 148,593.75

EMI on Loan of $ 234990 =  [244990*0.286%*(1+0.286%)^360]/[(1+0.286%)^360-1] = $ 1048.66

Total Interest Payment on Loan of $ 234990 = 1048.66*360 - 234990 = $ 142,528.45

Savings in Interest Expense due to $ 10,000 Down Payment = $ 148,593.75 - $ 142,528.45 = $ 6,065.30

Question No.d:

Total Rent Paid during 30 Years Period = 30*12*785 = $ 282,600