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# Annuity payment amounts with changing interest

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Set up a fund of semi-annual payments to be compounded semi-annually to accumulate a some of \$100,000 after 10 years at an 8 percent annual rate (20 payments). The 1st payment into the fund is to occur over 6 months starting today and the last payment is to take plae at the end of the 10th year.

a. Determine how much the semi-annual payment should be. (round to whole numbers.)

On the date after the 4th payment is made (beginning of the 3rd year) the interest rate will go up to a 10 percent annual rate, and you can earn a 10 percent annual rate on funds that have been accumulated as well as all future payments into the fund. Interest is to be compounded semi-annually on all funds.

b. Determine how much the revised semi-annual payments should be after this rate change (there are 16 payments and compounding dates). The next payment will be in the middle of the 3rd year. (Round all values to whole numbers).

#### Solution Summary

The solution explains how to calculate the annuity payment amounts with changing interest

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## Brian Robinson, Sam Gerhard, Cory Ponder, tony Jones, Echo Systems: bonds, stocks, payments, PV needed, Retiring.

Problem 1: Brian Robinson plans to to retire in exactly 35 years. His goal is to create a fund that will allow him to receive \$85,000 at the end of each year for the 30 years between retirement and death. You know that you will be able to earn 11% per year during the 30-year retirement period.

a. How much will you need today as a single amount to provide the fund calculated in part a if you earn only 9% per year during the 35 years preceding retirement?
b. How large a fund will you need when you retire in 35 years to provide the 30-year, \$85,000 retirement annuity?
c. What effect would an increase in the rate you can earn both during and prior to retirement have on the values found in parts a and b? Explain?

Problem 2: Sam Gerhart as part of his personal budgeting process, he has determined that in each of the next 5 years he will have budget shortfalls. In other words,he will need the amounts shown in the following table at the end of the given year to balance his budget: that is, to make inflows equal outflows. He expect to be able to earn 9 % on the investments during the next 5
years and wish to fund the budget shortfalls over the next 5 years with a single amount.

1. \$ 7,000
2. \$ 4,000
3. \$ 8,000
4. \$ 10,000
5. \$ 13,000

a. How large must the single deposit today into an account paying 7% annual interest be to provide for full coverage of the anticipated budget shortfalls?
b. What effect would an increase in your earnings rate have on the amount calculated in part a? Explain?

Problem 3: Cory Ponder borrowed \$25,000 at a 14% annual rate of interest to be repaid over 3 years. The loan is amortized into three equal, annual, end of
year payments.
a. Calculate the annual, end-of-year loan payment.
b. Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.

c. Explain why the interest portion of each payment declines with the passage of time.

Problem 4: Tony Jones is shopping for a used car. He has found one priced at
\$6,500. The dealer has told Tony that if he can come up with a down payment of
\$500, the dealer will finance the balance of the price at a 14% annual rate over 2 years (24 months).

a. Assuming that Tony accepts the dealer's offer, what will his monthly
(end-of-month) payment amount be?
b. What would Tony's monthly payment would be if the dealer were willing to finance the balance of the car price at a 9% annual rate.

Problem 5: Echo Systems has an outstanding issue of \$1,000-par-value bonds with a 12% coupon interest rate. The issue pays interest annually and has 16 years remaining to its maturity date.

1. If bonds of similar risk are currently earning a 10% rate of return, how much should the Parr Systems bond sell for today?
2. Describe the two possible reasons why similar-risk bonds are currently earning a return below the coupon interest rate on the Parr Systems bond.
3. If the required return were at 12% instead of 10%, what would the current value of Parr Systems' bond be? Contrast this finding with your findings in part a and discuss.

Problem 6: A company's common stock has paid a dividend of \$5.00 per share per year for the last 15 years. Management expects to continue to pay at that rate for the foreseeable future. Susan Talbot purchased 100 shares of class A common stock, 25 years ago at a time when the required rate of return for the stock was 14%. She wants to sell her shares today. The current required
rate of return for the stock is 12%. How much capital gain or loss will she have on her shares?

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