Question

5.  An annuity pays $20,000 per quarter for 25 years and the payments are made at the end of each quarter. The first payment is made at the end of the first quarter. If the annual interest rate is 8 percent compounded quarterly for the first 10 years, and 12 percent compounded quarterly thereafter, what is the present value of the annuity (i.e, value of the annuity now)?

6. Your objective is to have $4,000,000 in an account that earns 8% annual return when you retire in 40 years.

a) If you make an equal deposit at the end of every year to the account for the next 40 years, what is the annual deposit? Assume that your first deposit occurs at the end of next year.

b) You retire after 40 years and have $4,000,000 in the account as planned. You expect to live for another 25 years after retirement. Assume that you leave the $4,000,000 in the account that continues to earn 8% annual return.  You plan to make an equal withdrawal from the account every year for the next 25 years. The first withdrawal is made at the end of the first year after your retirement and the account balance would be depleted after you make the 25th How much can you withdraw at the end of each year for the next 25 years?

7. You have found your dream home. The selling price is $300,000. You will put $60,000 as down payment and obtain a 30-year fixed-rate mortgage loan at 4.5 percent annual interest rate for the rest.

a) You are required to make an equal payment every month for 360 months to pay off the balance on the loan. Assume that the first payment begins in one month after you obtained the loan. What will each monthly payment be?

b) If you want to pay off the remaining principal on your mortgage loan after 10 years (i.e., 120 months), how much will you have to pay? Assume that you have never missed your payments during the first ten years after you obtained the loan. The bank that you obtained the loan from imposes no charges for early payoff of the loan.

Answer 1

5)

The present value of the annuity is calculated using the following equation

Present value of the annuity = $ 797,789.54

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6)

a)

The equal annual deposit is found using the future value of annuity equation

In the above equation, the value of A is the annual deposit.

The annual deposit to be made equals $ 15440.65

b)

The amount that can be withdrawn each year is found using the present value of annuity equation, where the $ 4,000,000 is considered as present value of the withdrawls till the account balance is depleted.

In the above equation, the value of A is the amount that can be withdrawn annually.

Amount that can be withdrawn each year = $ 374715.1 $ 374715

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7)

a)

Size of the mortgage = Selling price of the home - downpayment

Size of the mortgage = $ 300000 - $ 60000 = $ 240000

The monthly payment is calculated using the following equation

Monthly payment = $ 1216.04

b)

Remaining balance on the loan = $ 192215.36