Prob 46 6 3 points You plan to purchase a 280000 house using

Prob. 4.6

6. (3 points) You plan to purchase a $280,000 house using a 30-year mortgage from your bank. Assume that the current 30-year mortgage rate is 4.25% and you will make a 15% percent down payment. Please use the financial calculator for these calculations and please do not include any multi-page amortization schedules! The answers to this question shouldn’t be more than one page!

a. Calculate the monthly payments on your mortgage, quoted to 2 decimal places, e.g. $1,056.74.

b. For each of the first three payments, calculate the amount of principal and interest paid for each payment.

c. Calculate the total interest paid over the first year (first 12 payments).

d. If you decide to move or refinance after 5 years, what is your balance owed (principal) on the loan?

e. If you decide to move after 15 years, what is your balance owed?    

Solution

Greetings,

A. Total Cost = 280000 Down Payment = 15% of 280000 = 42000

Therefore Loan Amount = 23800 Time = 30 Years Rate = 4.25%

In excel , installment is calculated as under -

=PMT(0.0425/12,360,238000,0,0) = $1170.82

B. For Ist oayment, interest = 238000*0.0425/12= 842.92

So balance is principal repayment = 1170.82-842.92= 327.90

So balance principal after Ist payment = 238000 - 327.90 = 237672.10.

So interest on second EMI = 237672.10*0.0425/12 = 841.76

So balance is the principal = 1170.82 - 841.76 = 329.06

Balance principal after second payment = 237672.10 - 329.06 = 237343.04

Interest on 3rd EMI = 237343.04*0.0425/12 = 840.59

So bal is principal = 1170.82 - 840.59 = 330.23

C. Principal outstanding at the end of 12 months can be calculated as under in excel -

=PV(0.0425/12,360-12,1170.82,0,0) = 233987.64. So principal payment by payment of 13 EMIs = 238000 - 233987.64 = 4012.36

Total of 12 EMIs = 1170.82*12 = 14049.84. So total interest payment = 14049.84 - 4012.36 = 10037.48

D. Balance outstanding after 5 years can be computer in the same manner as done in part C above -

Remaining Maturity = 25 years or 300 months

=PV(0.0425/12,300,1170.82,0,0) = 216122.32

E. Remaining maturity = 15 years or 180 months

=PV(0.0425/12,180,1170.82,0,0) = 155636.12