# Time Value of Money and Bond Calculations (14 problems)

Note: Unless otherwise stated, assume that interest is calculated on an annual basis

1) Ian invests $1000 today in a 3 year CD paying 3.75% annually. He receives the full amount of principal and accrued interest in 3 years. How much will he receive in 2 years?

N i PV PMT FV

2) How much would Sylvia have to invest in a CD today to receive $1225 in 4 years time if the interest rate payable on the CD is 2.10%

N i PV PMT FV

3) A zero coupon bond is sold at a discount and pays no interest during its life. John invests $900 in zero coupon bond which promises to pay $1100 in 5 years time. What is the rate of return on the investment?

N i PV PMT FV

4) Maggie has the opportunity to invest $1000 in a 5 year CD. She has the option to receive a 4.65% return, compounded quarterly, 4.75% compounded semi-annually, or 4.85% compounded annually. What option will give her the highest total return and how much will she receive in 5 years time?

Quarterly

N i PV PMT FV

Semi-annually

N i PV PMT FV

Annually

N i PV PMT FV

5) Chris invests $1000 in a 10 year ordinary annuity when prevailing interest rates are 3.5%. How much will he receive annually?

N i PV PMT FV

6) Using the calculator and the Rule of 72s, how long will it take a $4000 investment to double if the interest rate is 7.3%?

Calculator Method

N i PV PMT FV

Rule of 72s

7a) Helena purchases a condo and obtains a $250,000 fully amortizing level payment 15 year mortgage bearing an (annual) interest rate of 6.75%. How much will her monthly blended principal and interest payment be?

N i PV PMT FV

7b) For months 1,2 and 3 of the mortgage, determine how much of the total payment is principal and how much is interest and construct an amortization table

Month Beginning

Principal Payment Interest Amortization of Principal Ending Principal

1 250000

2

3

8) Johnson Corp is considering a capex project that will require an investment of $150,000. It will have a 5 year lifetime and will return the following amounts:

Year 1 $20,000

Year 2 $25,000

Year 3 $80,000

Year 4 $70,000

Year 5 $30,000

8a) If at the end of year 5 the project has no salvage value, what is the company's expected annual rate of return (IRR)?

8b) If at the end of year 5 the project has a salvage value of $20,000, what is the company's expected annual rate of return? [Hint: The salvage value will add to the cash flow that Johnson receives in year 5]

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#### Solution Preview

The following answers have been explained in detail and the inputs into the financial calculator have been shown step by step in the attached files.

1) FV in 2 years = $1,076.41

2) PV = $1,127.28

3) I = ...

#### Solution Summary

This solution consists of 8 time value of money (TVM) problems and 6 bond value problems. The numerical inputs into the financial calculator are shown in detail, with some added explanations. The TVM problems include the calculations of present value, rate of return, future value with different compounding periods, amortization basics, and cash flow example. The bond value problems include the calculation of a current value of a bond with different compounding periods, bond yield, and the relative sensitivity of bond prices to changes in interest rate.

Finance Problems (calculating original principal amount, present value, and more...)

1. Hayley makes annual end-of-year payments of $6,260.96 on a five-year loan with an 8 percent interest rate. The original principal amount was

1. $25,000.

2. $30,000.

3. $31,000.

4. $20,000.

2.Nico makes annual end-of-year payments of $5,043.71 on a four-year loan with an interest rate of 13 percent. The original principal amount was

1. $24,462.

2. $20,175.

3. $ 3,092.

4. $15,000.

3.If a United States Savings bond can be purchased for $29.50 and has a maturity value at the end of 25 years of $100, what is the annual rate of return on the bond?

1. 5 percent

2. 6 percent

3. 8 percent

4. 7 percent

4.The present value of a $25,000 perpetuity at a 14 percent discount rate is

1. $350,000.

2. $219,298.

3. $285,000.

4. $178,571.

5.Jia borrows $50,000 at 10 percent annually compounded interest to be repaid in four equal annual installments. The actual end-of-year loan payment is

1. $10,774.

2. $15,773.

3. $14,340.

4. $12,500.