Question

After considerable negotiation with its owners, you have purchased a home for $625, 000. After a 20 percent down payment, you finance the remainder under a twenty-year mortgage at the annual percentage rate (APR) of 3.76%).

a. What are your monthly payments? Show ALL your work, including your use of the formula.

b. Over time, what is the total cost of the home? After the second monthly payment, what is the total amount that you owe each in interest and principal? (Note: The “total” amount is the total amount of the loan split into the total amount of interest and the total amount of principal.) Show ALL your work, including your use of the formulas. (Note: In the intermediate steps of your calculations, take the decimal point to four places. At the final calculation, round off to two places.)

Answer 1

The amount of Loan = 625000*(1-20%) = 500,000
a. Rate Per month = 3.76%/12
Number of Periods = 12*20 = 240
Monthly Payment = PV/(1-(1+r)^-n)/r = 500000/(1-(1+3.76%/12)^-240)/(3.76%/12) = 2967.04

b. Total Cost of the home = Number of Periods * PMT = 240*2967.04 = 712,090.64

c. Interest in first month = 500000*3.76%/12 = 1566.67
Principal Part of PMT = 2967.04 -1566.67 = 1400.38
Principal remaining after 1 month =  500,000 -1400.38 = 498,599.62

Interest part in second month = 498,599.62*3.76%/12 = 1562.28
Principal Part in second month = 2967.04 - 1562.28 = 1404.77

All calculation done without rounding off

Please Discuss in case of Doubt

Best of Luck. God Bless
Please Rate Well