Time value of money is useful in making informed business decisions. For example the “net present value method” can be used to help decide the best alternative among multiple alternative uses of a firm or personal financial resources. By discounting various alternatives to their “present value” one can compare the alternatives. Time value of money can also answer such questions as what one’s investment will be worth at a certain point of time in the future, assuming a certain interest rate. Time value of money can also be used to compute such useful information as car, mortgage and other loan payments. Another use of time value of money in accounting is reporting of certain long-term assets and liabilities.

Time value of money is based on the principle of compound interest. Each time there is a compounding period the new principal is increased by the interest from the previous period.

Converting Before Using the Tables

When using the tables, you may need to convert if, for example, in a lump sum situation there are more than one compounding periods in a year. Or you may need to convert (to monthly compounding) if, for example, you are working with an annuity situation involving a car loan that involves monthly rather than annual periodic payments.

You often need to convert whether it is a lump sum or an annuity situation. Do the following conversions before using the tables. See some of the examples which follow these notes.

For semi-annual compounding [or for deposits every six months in an annuity], take the annual interest rate and divide it by 2. Take the number of years and multiply by 2.

For quarterly compounding [or for quarterly deposits in an annuity] take the annual interest rate and divide it by 4. Take the number of years and multiply by 4.

For monthly compounding [or for monthly deposits in an annuity] take the annual interest rate and divide it by 12. Take the number of years and multiply by 12.

Lump Sum Amounts

Future Value of $1 = Present Value X Future Value of $1 Table Factor

Present Value of $1= Future Value X Present Value of $1 Table Factor

Use the $1 table when you are dealing only with a lump sum amount. (However when you have an annuity in the problem, do not use the lump sum table; instead use the annuity table. Use the annuity table even if you are looking for a lump sum, as shown in No. 4 which follows these notes.)

Notice that there are four variables with lump sum situations: Present Value, Future Value, Interest Rate, and Period. You need to know three out of the four to figure out an unknown. You saw above how to compute Present Value and Future Value. Now suppose you want to find the interest rate.

Present Value Approach: PV / FV = computed PV Table factor Go to the PV table. Where the table factor and periods intersect is the interest rate.

Use this same approach to figure the number of periods when you know the interest rate and PV and FV.

Annuities

An annuity means a series of equal periodic “deposits,” or “rents” which can be either payments or receipts; they are made at equal periodic intervals. Use the annuity tables when you are dealing with equal periodic payments or receipts at equal periodic intervals.

Use Ordinary Annuity table for payments made at the end of the period. Use Annuity Due table for payments made at the beginning of the period.

Future Value of an Annuity = Annuity Deposit X Future Amount of an Annuity Table factor.

Present Value of an Annuity = Annuity Deposit X PV of Annuity Table Factor Note the Annuity Deposit may be either a payment or receipt.

Now say you wish to find the amount of the deposit, which could be either a periodic payment like a car or mortgage payment, or a periodic receipt such winnings from the lottery or more realistically monthly withdrawls of cash during retirement.

Rent or Payment/Receipt = PV / PV of annuity table factor or

Rent or Payment/Receipt = FV / FV of annuity table factor

You cannot just use either of the PV or FV approaches. Use the PV approach if PV is the given information. You would have to use the FV approach if FV is the given information. Often you use the present value approach though. For example if you are buying a car and want to figure out the car payments, the current price of the car is “Present Value.” It is assumed to be the “cash-equivalent” price.

A Few Practice Problems

1. You want to know how much you should deposit in the bank each month in order to have $10,000 in four years. What type of problem is this?

A. present value of an annuity

B. present value of an amount

C. future value of an annuity

D. future value of an amount

The correct answer is C. First you know this is an annuity because it involves equal periodic payments to the bank at equal intervals. You know it is future value because you are asked to find what future amount your annuity will grow to. Even though it is growing to a single amount, be sure to note that you are looking for the future value of an ANNUITY.

2. You want to know how much you should deposit in the bank now in order to have $10,000 in four years. What type of problem is this?

A. present value of an annuity

B. present value of an amount

C. future value of an annuity

D. future value of an amount

The correct answer is B.

3. Someone will pay you $10,000 in four years. You want to know how much it is worth to you now, assuming a certain interest rate. What kind of problem is this?

A. present value of an annuity

B. present value of an amount

C. future value of an annuity

D. future value of an amount

The correct answer is B.

4. What single amount do you have to deposit in the bank now in order to be able to withraw $200 a month for the next five years? What kind of a problem is this? A. present value of an annuity

B. present value of an amount

C. future value of an annuity

D. future value of an amount

The answer is A. Even though a single amount will be deposited, it is still an annuity problem. Hint: any time a problem involves equal periodic payments, use an annuity table.

5. When you were born your parents set up a trust fund designed to accumulate $88,000 by the time you are 50 years old. You are 34 years old today. If you negotiate getting the money today, what will you get? Assume an 8% interest rate and annual compounding.

First realize you are looking for present value. “Today” and “now” are hints you want present value. Next realize you need to subtract your current age for 50 years to get the number of years, which would be 16 years in this problem.

So PV = FV X PV table factor for 8% and 16 years 25,687 = 88,000 X .2919

6. You are very rich and will be retired soon. You want to take out $416,000 every six months for 6 years. You can get a 6% interest rate. How much do you need to deposit in the bank today to make this happen?

You are looking for the Present Value of an annuity , since you want the amount to deposit TODAY, and you will be withdrawing equal periodic payments. So use the annuity table even though you are putting a lump sum in the bank.

PV annuity = Deposit X PV annuity factor ( 3%, 12 semi-annual periods) = 416,000 X 9.9540

= 4,140,864, the amount you need to deposit today.

7. Trego County wants to raise $4,000,000 to finance the construction of a new high school. The school board wants to make semiannual payments to repay the loan over the next 15 years. What will be the amount of the payments assuming the interest rate of 10%?