Chapter B, Problem 19E

To determine

Introduction:

Present value:

The present value of a future amount is the worth of the future amount in the present time. The value of an amount today is not the same as the amount tomorrow or in some future date. The worth /value of an amount changes with time as the amount has a time value. The present value of a future amount is calculated by discounting back the future amount to the present, considering the discount rate and the time period for which the amount is discounted as shown below.

  $\mathrm{Pr}esentvalue=Futurevalue\times \frac{1}{{\left(1+\mathrm{int}erestrate\right)}^{timeperiod}}$

Without applying this formula, the present value is calculated by using the present table. Here, present value is calculated by multiplying the future amount with the present discount factor. The present discount factor depends on the discount rate (i) and the time period (n) and it is found from the present table. The present table provides present discount factor for different values of the discount rate (i) and the time period (n).

Future value:

The future value of a present amount is the worth of the present amount in the future time. The value of an amount today is not the same as the amount tomorrow or in some future date. The worth /value of an amount changes with time as the amount has a time value. The future value of a present amount is calculated by considering the discount rate/interest rate and the time period for which the amount is discounted as shown below.

  $Futurevalue=\mathrm{Pr}esentvalue\times {\left(1+\mathrm{int}erestrate\right)}^{timeperiod}$

Without applying this formula, the future value is calculated by using the future table. Here, future value is calculated by multiplying the present amount with the future discount factor. The future discount factor depends on the discount rate (i) and the time period (n) and it is found from the future table. The future table provides future discount factor for different values of the discount rate (i) and the time period (n).

Compounding:

Compounding refers to the process where principal amount along with interest is assumed to be reinvested and earnings are made on them. Here, interest payment is made more than once per annum.

Annuity:

An annuity is a series of equal amounts, paid on an equal time periods.

To identify:

The given cases related to

1. a) Present value or a future value b) a single amount or an annuity
2. Table used in computation
3. Interest rate and time period to be used