Return

Below are shown some simple time value problems you can use for practice:

1. You are interested in a bond with a coupon rate of 8%, with interest paid semi-annually, that has 9 years until maturity. The bonds have a $1000 par value and bonds of this quality are currently yielding 9.25% in the market. What is the price of the bond?

Begin by calculating the cash interest received semi-annually; 8%/2 * $1000 = $40 per period

The bond has 18 semi-annual periods until maturity and you want to earn 9.25% / 2 or 4.625% per period

n 18
i 4.625
PV ?
PMT 40
FV 1000

Solve for PV = $924.75 which is the maximum price you would pay for the bond.

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2. You have an opportunity to buy a bond at a price of 937.50 which has 7 years until it matures, pays semi-annual interest based on a 7.125% annual rate and has a par value of $1000.00. What would be your return or yield to maturity?

Adjust your time periods to semi-annual; 7 * 2 = 14; adjust coupon rate to semi-annual; 7.125% / 2 = 3.5625%

Find semi-annual interest to be received; 3.5625% * 1000 = $35.625

n 14
i ?
PV -937.50
PMT 35.625
FV 1000

Solve for i = 4.1605%. Remember this is semi-annual so multiply by 2 to get an annual rate of 8.32%

Note: If you got an "Error 5" message, it means you forgot to put the minus sign in front of the PV or outflow

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3. What is the monthly payment on a 15 year mortgage of $200,000 at a rate of 5.75%?

n will be 15 years * 12 months = 180 periods

The monthly interest rate is 5.75% / 12 = .47917% per month (This is not technically correct under the premise of compound interest since that rate per month would be equivalent to 5.9% per year, but the APR is done using simple division and multiplication so we will use it here.)

n 180
i .47917
PV 200000
PMT ?
FV 0

The PMT or monthly payment would be $1,660.82. Note that putting the FV at 0 implies we are fully amortizing the loan and there will be no balloon payment at the end. Also, note that your answer came as a minus number which is consistent with entering the PV as a positive number. That is the inflow you are receiving in exchange for making the outflows each month.

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4. You would like to acquire a new pickup truck while pursuing your studies. The local dealer has one you like for the paltry sum of $22,000 and has offered you a deal where you pay only $250.00 per month and 8.5% annual interest for five years with a balloon payment at the last month of the contract. What is the amount of the last payment?

Don't laugh; I got this example from a student who did just this!

n 60
i .708333
PV -22000
PMT 250
FV ?

FV = $14,990.00

Add the normal payment of $250 and you would owe a mere $15,240.00 in month 60!

We won't even go near the subject of paying this amount in month 60 for a five year old pickup truck driven by a college student! Gives a whole new meaning to the term: "under-water". Of course, by then he will have graduated and probably be the CEO of a Fortune 500 company so it should not be a problem. :-)

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5. You are borrowing $10,000 for some minor home improvements. Current interest rates on home improvement loans = 9% and you feel comfortable paying $250.00 per month to retire this debt. How long will it take to pay the loan balance down to zero?

n ?
i .75
PV -10000
PMT 250
FV 0

n = 48 periods or months which is equivalent to 4 years.

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You might have noticed that each of the five problems solved for a different unknown such as price (PV) or return (i). The purpose was to illustrate that the calculator is indifferent as to which variable you are attempting to solve. The simple rule is: "load four and solve for the fifth" and you might have noticed that where the problem did not indicate a specific amount for one of the four variables, I was careful to enter the value of zero so the calculator knew it was one of the four known variables. It cannot solve for two unknowns at a time so you have to supply it with something for each of the four known quantities even if that 'something' is a zero.