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ANEK [815]
3 years ago
15

Mortgages, loans taken to purchase a property, involve regular payments at fixed intervals and are treated as reverse annuities.

Mortgages are the reverse of annuities, because you get a lump-sum amount as a loan in the beginning, and then you make monthly payments to the lender. You’ve decided to buy a house that is valued at $1 million. You have $100,000 to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $900,000 mortgage, and is offering a standard 30-year mortgage at a 12% fixed nominal interest rate (called the loan’s annual percentage rate or APR). Under this loan proposal, your mortgage payment will be per month. (Note: Round the final value of any interest rate used to four decimal places.)
Business
1 answer:
storchak [24]3 years ago
6 0

Answer:

Ans. your monthly payment, for 30 years is $9,257.51 if you buy a property worth $1,000,000 and you make a down payment of $100,000

Explanation:

Hi, first we have to change the fixed rate in terms of an effective monthly rate, which is 1% effective monthly (12% nominal interest/12 =1% effective monthly). After that, take into account that the property is going to be paid in 30 years, but since the payments are going to be made in a montlhly basis, we have to turn years into months (30 years * 12 = 360 months).

After all that is done, all we have to do is to solve the following equiation for "A".

PresentValue=\frac{A((1+r)^{n} -1)}{r(1+r)^{n} }

Where:

A= Annuity or monthly payment

r= Rate (effective monthly, in our case)

n= Periods to pay (360 months)

Everything should look like this.

900,000=\frac{A((1+0.01)^{360} -1}{0.01(1+0.0.1)^{360} }

900,000=A(97.2183311)

\frac{900,000}{97.2183311} =A

A=9,257.51

Best of luck.

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L bond has a coupon rate of 9 percent, a face value of $1,000 and matures in 15 years. The coupon payments are made on annual basis. At the time of maturity the bondholder gets the face value.

We can find the present value of the coupon payments using the present value of annuity formula and the present value of the face value to be received after fifteen years using the present value formula. Sum of the present value of annuity of coupon payments and present value of the face value should equal the fair value (price) of the bond.

If the required rate of return is 5 percent, the price of the bond can be computed as under

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