calculate the mortgage interest rate

calculate the mortgage interest rate

AFM 121-Jason has just signed a contract under which
Subject: Business    / Finance   
Question

Jason has just signed a contract under which he will receive payments over the next five years. Each payment will be in the amount of $3,000, and there will be six payments per year. The payments will be made at the end of the second, fourth, sixth, eighth, tenth and twelfth months in each of the five years. If the stated annual interest rate is 6% APR with annual compounding, and the first payment is two months from today, what is the present value of Jason’s contract?

4 Two years ago, you purchased a $20,000 car, putting $4,000 down and borrowing the rest. Your loan was a 48-month fixed rate loan at a stated rate of 6% per year (APR compounded monthly). You paid a non-refundable application fee of $100 at that time in cash. Interest rates have fallen during the last two years and a new bank now offers to refinance your car by lending you the balance due at a stated rate of 4% per year (APR compounded monthly). You will use the proceeds of this loan to pay off the old loan. Suppose the new loan requires a $200 non-refundable application fee. Given all this information, should you refinance? How much do you gain/lose if you do?

5 Lu Xun and Yu Ling and bought a house in Kitchener exactly 5 years ago. They took out a mortgage for $400,000 at that time. The mortgage had a 25-year amortization period and a quoted interest rate of 8%. They then decided to buy a new house in Waterloo. Today they will receive payment from the buyer of their old home and make a down payment on the new house. If the old house sold for $600,000, the new one is priced at $800,000, and the down payment on the new house equals the net proceeds from the sale of their old house, how big is their new mortgage? (Net proceeds= Selling Price of old house less Outstanding Principal Balance on the old mortgage) If the new mortgage has a quoted interest of 6% (APR, semi-annual compounding) and a 20-year amortization period, how big are Steve and Laurie’s new monthly payments?

7 The Madans live in Kitchener and they bought their house exactly four years ago. They made a 25%b down payment at the time. Their monthly mortgage payments are $2,000 and they will have to keep paying their mortgage for 26 more years. The interest rate on their mortgage is 5.5839% ( APR with monthly compounding).

a. How much did the Madans pay for their house four years ago? /3

b. The Madans have just made their most recent monthly mortgage payment of $2,000 (the 48th). How much do the Madans still owe on their mortgage after four years of payments? /3

c. c. Their financial planner advises the Madans to switch from monthly to bi-weekly mortgage payments which they may do with no penalty. What would be the new bi-weekly mortgage payment assuming the 48th payment has just been made and the effective interest rate remains the same? (Assume that there are exactly 52 weeks per year.) /3

8 Please calculate the duration and volatility on a bond where the principal is $1.000 and the annual coupon rate is 4 percent and paid annually. The inflation is 2 percent and the market interest rate is 8 percent. /4