Question

1) You have just purchased a home and taken out a $ 530,000 mortgage. The mortgage has a 30​-year term with monthly payments and an APR of 5.20%.

a. How much will you pay in​ interest, and how much will you pay in​ principal, during the first​ year?

b. How much will you pay in​ interest, and how much will you pay in​ principal, during the 20th year​ (i.e., between 19 and 20 years from​ now)?

2) You need a new car and the dealer has offered you a price of $20,000​, with the following payment​ options: (a) pay cash and receive a $2,000 rebate, or​ (b) pay a $5,000 down payment and finance the rest with a 0% APR loan over 30 months. But having just quit your job and started an MBA​ program, you are in debt and you expect to be in debt for at least the next 2​ ½ years. You plan to use credit cards to pay your​ expenses; luckily you have one with a low​ (fixed) rate of 13.59% APR. Which payment option is best for​ you?

3) The mortgage on your house is five years old. It required monthly payments of $1,450​, had an original term of 30​ years, and had an interest rate of 10% (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 6.625% (APR).

a. What monthly repayments will be required with the new​ loan?

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

c. Suppose you are willing to continue making monthly payments of $1,450. How long will it take you to pay off the mortgage after​ refinancing?

d. Suppose you are willing to continue making monthly payments of $1,450 and want to pay off the mortgage in 25 years. How much additional cash can you borrow today as part of the​ refinancing?

4) Your uncle Fred just purchased a new boat. He brags to you about the low 6.9% interest rate​ (APR, monthly​ compounding) he obtained from the dealer. The rate is even lower than the rate he could have obtained on his home equity loan 7.9% ​APR, monthly​ compounding). But if his tax rate is 25% and the interest on the home equity loan is tax​ deductible, which loan is truly​ cheaper?

Answer 1

1) Given,

Loan amount = $ 530000

Term = 30 years

Term in months (n) = 30 x 12 = 360 months

APR = 5.2%

APR monthly (r) = 5.2/12 = 0.4333% or 0.004333

Solution : -