# Time Value of Money

Please see the attached file.

1. I am getting ready to buy a new car. I plan on spending $35,000 for the car and I believe my current car has a $17,000 trade-in value and I make no additional downpayment. I keep my vehicles 5 years but would like a three-year loan.

What will my monthly car payment be at the end of each month if the annual interest rate is 12%?

2. My firm is hunkering down and we anticipate a long tough year. We believe that over the winter months, we will need the following funds:

End of Month Shortfall

November $25,000

December $30,000

January $32,000

February $28,000

March $15,000

(a) We are coming off the summer flush with cash by the end of October. How much should we make as a single deposit today to cover the budget shortfalls next winter if we can earn 12% annually on the funds?

(b) If we could earn more than 12% on the funds, what effect would that have on the amount of the single deposit we make today?

3. My husband and I are planning to retire in exactly 10 years. Considering our social security benefits and income from other investments, we have decided that we will need an additional $35,000 per year to be able to travel and explore the world. We believe that we will need these funds for 25 years following retirement (after that, we've got long-term care insurance). We anticipate earning 7% on our retirement funds for the 25 years we'll be active and retired and would like this money available at the end of each year.

We don't want to worry about depositing into this fund after we retire 10 years from now.

(a) How much must our fund be when we retire in 10 years to provide our 25-year, $35,000 annuity with no worries?

(b) My husband and I discussed things further and decided that we want to set aside the amount we will need to have in the fund today to get it out of the way and we won't have to worry about anything. How much will we need if we can earn 4% on those funds from now through our 10 years-from-now retirement plan?

(c) What effect would an increase in the rate we can earn both during and prior to retirement have on the values you calculated in (a) and (b)? Explain fully!

4. My firm has an outstanding issue of $1,000 par-value bonds with a 7% coupon interest rate. We pay interest on this issue annually and we have 10 years to its maturity date.

(a) If bonds of similar risk are currently earning a 5% rate of return, how much should our bonds sell for today?

(b) Why would bonds with similar risk to ours be currently earning a return below our 7% coupon interest rate?

(c) What would the current value of our bond be if the required return were at 7% instead of 5%? Contrast this finding with your results from (a) above and explain.

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#### Solution Preview

Please see the attachment.

Problem Set 3

Please answer the following questions in the space provided. You may insert additional lines as necessary in order to complete your response fully.

1. I am getting ready to buy a new car. I plan on spending $35,000 for the car and I believe my current car has a $17,000 trade-in value and I make no additional downpayment. I keep my vehicles 5 years but would like a three-year loan.

What will my monthly car payment be at the end of each month if the annual interest rate is 12%?

The amount of loan = 35,000-17,000 (value of old car) = 18,000

Period of loan = 3X12=36 months

Rate = 12%/12 = 1% per month

The monthly payments would be such that the present value of the payments is equal to the loan amount. The monthly payments would be in the form of an annuity. We use the PV of annuity formula to get the monthly payments.

PV = PMT [(1 - (1 / (1 + i)^n)) / i]

where

PV = loan amount = 18,000

PMT = monthly payment

i = interest rate = 1%

n = period = 36 months

18,000 = PMT [(1-(1/(1+1%)^36))/1%]

PMT = $597.86

The monthly payment is $597.86

2. My firm is hunkering down and we anticipate a long tough year. We believe that over the winter months, we will need the following funds:

End of Month Shortfall

November $25,000

December $30,000

January $32,000

February $28,000

March $15,000

(a) We are coming off the summer flush with cash by the end of October. How much should we make as a single deposit today to cover the budget shortfalls next winter if we can earn 12% annually on the ...

#### Solution Summary

The solution explains some questions relating to Time Value of Money.