Time value of money is utile in doing informed concern determinations. For illustration the “net present value method” can be used to assist make up one’s mind the best option among multiple alternate utilizations of a house or personal fiscal resources. By dismissing assorted options to their “present value” one can compare the options. Time value of money can besides reply such inquiries as what one’s investing will be deserving at a certain point of clip in the hereafter. presuming a certain involvement rate. Time value of money can besides be used to calculate such utile information as auto. mortgage and other loan payments. Another usage of clip value of money in accounting is describing of certain long-run assets and liabilities.

Time value of money is based on the rule of compound involvement. Each clip there is a compounding period the new principal is increased by the involvement from the old period.

Converting Before Using the Tables

When utilizing the tabular arraies. you may necessitate to change over if. for illustration. in a ball amount state of affairs there are more than one intensifying periods in a twelvemonth. Or you may necessitate to change over ( to monthly intensifying ) if. for illustration. you are working with an rente state of affairs affecting a auto loan that involves monthly instead than one-year periodic payments.

You frequently need to change over whether it is a lump amount or an rente state of affairs. Make the undermentioned transitions before utilizing the tabular arraies. See some of the illustrations which follow these notes.

For semi-annual combination [ or for sedimentations every six months in an rente ] . take the one-year involvement rate and split it by 2. Take the figure of old ages and multiply by 2.

For quarterly intensifying [ or for quarterly sedimentations in an rente ] take the one-year involvement rate and split it by 4. Take the figure of old ages and multiply by 4.

For monthly intensifying [ or for monthly sedimentations in an rente ] take the one-year involvement rate and split it by 12. Take the figure of old ages and multiply by 12.

Lump Sum Sums

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 tabular array when you are covering merely with a ball amount sum. ( However when you have an rente in the job. make non utilize the ball amount tabular array ; alternatively use the rente tabular array. Use the rente tabular array even if you are looking for a ball amount. as shown in No. 4 which follows these notes. )

Notice that there are four variables with ball amount state of affairss: Present Value. Future Value. Interest Rate. and Period. You need to cognize three out of the four to calculate out an unknown. You saw above how to calculate Present Value and Future Value. Now suppose you want to happen the involvement rate.

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

Use this same attack to calculate the figure of periods when you know the involvement rate and PV and FV.

Annuities

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

Use Ordinary Annuity tabular array for payments made at the terminal of the period. Use Annuity Due tabular array 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 reception.

Now say you wish to happen the sum of the sedimentation. which could be either a periodic payment like a auto or mortgage payment. or a periodic reception such profitss from the lottery or more realistically monthly withdrawls of hard currency during retirement.

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

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

You can non merely utilize either of the PV or FV attacks. Use the PV attack if PV is the given information. You would hold to utilize the FV attack if FV is the given information. Often you use the present value attack though. For illustration if you are purchasing a auto and want to calculate out the auto payments. the current monetary value of the auto is “Present Value. ” It is assumed to be the “cash-equivalent” monetary value.

A Few Practice Problems

1. You want to cognize how much you should lodge in the bank each month in order to hold $ 10. 000 in four old ages. What type of job is this?

A. present value of an rente

B. present value of an sum

C. future value of an rente

D. future value of an sum

The right reply is C. First you know this is an rente because it involves equal periodic payments to the bank at equal intervals. You know it is future value because you are asked to happen what future amount your rente will turn to. Even though it is turning to a individual sum. be certain to observe that you are looking for the future value of an ANNUITY.

2. You want to cognize how much you should lodge in the bank now in order to hold $ 10. 000 in four old ages. What type of job is this?

A. present value of an rente

B. present value of an sum

C. future value of an rente

D. future value of an sum

The right reply is B.

3. Person will pay you $ 10. 000 in four old ages. You want to cognize how much it is deserving to you now. presuming a certain involvement rate. What sort of job is this?

A. present value of an rente

B. present value of an sum

C. future value of an rente

D. future value of an sum

The right reply is B.

4. What individual sum do you hold to lodge in the bank now in order to be able to withraw $ 200 a month for the following five old ages? What sort of a job is this? A. present value of an rente

B. present value of an sum

C. future value of an rente

D. future value of an sum

The reply is A. Even though a individual sum will be deposited. it is still an rente job. Hint: any clip a job involves equal periodic payments. utilize an rente tabular array.

5. When you were born your parents put up a trust fund designed to roll up $ 88. 000 by the clip you are 50 old ages old. You are 34 old ages old today. If you negotiate acquiring the money today. what will you acquire? Assume an 8 % involvement rate and one-year combination.

First recognize you are looking for present value. “Today” and “now” are intimations you want present value. Following realize you need to deduct your current age for 50 old ages to acquire the figure of old ages. which would be 16 old ages in this job.

So PV = FV X PV table factor for 8 % and 16 old ages 25. 687 = 88. 000 Ten. 2919

6. You are really rich and will be retired shortly. You want to take out $ 416. 000 every six months for 6 old ages. You can acquire a 6 % involvement rate. How much do you necessitate to lodge in the bank today to do this go on?

You are looking for the Present Value of an rente. since you want the sum to lodge TODAY. and you will be retreating equal periodic payments. So use the rente table even though you are seting a ball amount in the bank.

PV rente = Deposit X PV rente factor ( 3 % . 12 semi-annual periods ) = 416. 000 Ten 9. 9540

= 4. 140. 864. the sum you need to lodge today.

7. Trego County wants to raise $ 4. 000. 000 to finance the building of a new high school. The school board wants to do biannual payments to refund the loan over the following 15 old ages. What will be the sum of the payments presuming the involvement rate of 10 % ?