Question

The mortgage on your house is five years old. It required monthly payments of SEK 12,000, had an original term of 30 years, and had an interest rate of 6.5% (APR). In the intervening five years, interest rates have fallen and so you have decided to refinance - that is, you will roll over the outstanding balance into a new mortgage. The new mortgage has a 30-year term, requires monthly payments, and has an interest rate of 3.5% (APR).

(a) What monthly repayments will be required with the new loan?

The new monthly payments will be SEK . (round to full SEK)

(b) If you still want to pay off the mortgage in 25 years, what monthly payment should you make after you refinance?

The monthly payments will be in this case SEK . (round to full SEK)

(c) Suppose you are willing to continue making monthly payments of SEK 12,000. How long will it take you to pay off the mortgage after refinancing?

Paying off the mortgage will take months. (round to full months)

(d) Suppose you are willing to continue making monthly payments of SEK 12,000, and want to pay off the mortgage in 25 years. How much additional cash can you borrow today as part of the refinancing?

Additional cash that you can borrow is SEK . (round to full SEK)

Answer 1

The old mortgage had an original term of 30 years and now after 5 years, 25 years are remaining. This mortgage had a interest rate of 6.5% and monthly payments of SEK 12,000.

Annuity is a series of cash flows of a certain amount and for a certain time period specified. The mortgage is an annuity with monthly payments.

The formula for present value of annuity is as follows :-

Present Value of Annuity = PMT * 1-(1+r)-

were, PMT = Periodic Payment

r = Rate of Interest for a period

n = Number of periods

Thus, the balance of loan after 5 years is :-

Present Value of Original Loan = 12000 *= 00*1- (1 + (0.065/12))-25+12) (0.065/12)

Present Value of Original Loan = 12000 * 00*1- (1 + (0.0054))-(300) (0.0054)

Present Value of Original Loan = SEK 17,77,232.34

a. The new loan has an interest rate of 3.50% per annum and a term of 30 years.

The present value of original loan will be the amount of new loan taken. Thus, we have to find the periodic payments for new loan.

17,77,232 = PMT *-(1 + (0.035/12))-(3012) (0.035/12)

1-(1 + (0.0029))-(360) 17,77,232 = PMT * (0.0029)

PMT = 7,980.57 = SEK 7,981.

Thus, monthly payments of SEK 7,981 will be required for new loan.

b. If the new loan is for 25 years instead of 30 years, then

17,77,232 = PMT * DMT1-(1 + (0.0029))-(25+12) (0.0029)

17,77.232 = PMT * DMT1-(1 + (0.0029))-(300) (0.0029)

PMT = 8,897.24 = SEK 8,897.

Thus, the monthly payment for new loan with 25 years tenure will be SEK 8,897.

c. If monthly payments of SEK 12,000 are made, then

17.77.232 = 12.000 * _ 1-(1+ (0.00295)- (0.0029)

n = number of months required to repay the loan

17.77.232 | 12,000 1-(1+ (0.00291) - (0.0029)

0.4320 =1-(1.0029)

1-0.4320 = (1.0029)--

0.5680 = (1.0029) 7.

n = 194 months

Thus, it will take 194 months to repay the mortgage.

d. The monthly payments are SEK 12,000 for 25 years. We find out the present value of annuity which will be the total amount of new loan.

New loan Amount = 12.000 *1- (1 + (0.0029) - (25+12) (0.0029)

New loan Amount = 12,000 * 000*1-(1 + (0.0029))-(300) (0.0029)

New loan Amount = 23,97,010.59

New loan Amount = SEK 23,97,010.

Thus,

Additional loan = New loan Amount - Present value of Original loan

Additional loan = 23,97,010 - 17,77,232

Additional loan = SEK 6,19,778

Thus, if you make monthly payment of SEK 12,000 for 25 years, you get additional loan of SEK 6,19,778.