# Time value of money

**Introduction**

Time value of money is the basic concept of finance which says that value of money as of today is more than value of money in the future period.

To calculate time value of money we have two methods;

- Compounding
- Discounting

**Time value of money – Compounding**

Compounding is the estimate of future cash flows that shall arise when any sum of amount is invested at a given interest rate for a given time period.

An amount that is invested today is multiplied by compound factor to arrive at future cash flows at specific interest rate.

Where:

- i = interest rate
- n = number of years

**Example 1:**

A company wants to invest Rs.100,000 at 12% interest for a period of 5 years, calculate future value which the company shall get after 5 years.

100,000 x ( 1 + 12% ) ^{5}

Rs.176,234 is the future value.

**Time value of money – discounting**

Discounting is the estimate of present value of future cash flows at specific time in the future at a given interest rate.Â

An amount expected at future time is multiplied by discount factor to arrive at the present value at specific interest rate.

Present value = Amount today xÂ ( 1 + i ) – ^{5}

**Example 2:**

A company wants Rs.176,234 in 5 year time period, it has an investment opportunity at interest rate of 12%. How much to be invested now to get this amount after 5 years.

176,234 x ( 1 + i) – ^{5}

Rs.100,000 is the amount to be invested now to get Rs.176,234 in 5 years.

**Example 3:**

A person has borrowed Rs.150,000 for the period of 3 years. He has given an offer that he shall pay Rs.25,000 further if loan is extended for further two year to make total loan period of 5 years. Interest rate is 8%. Now suggest is it feasible to accept the offer or not.

**Answer:**

Present value = Amount today x ( 1 + i) – ^{n}

= 150,000 x ( 1 + 0.07) – ^{3}

= 122,444

**Or option 2**

Â = 150,000 + 25,000 = 175,000 x ( 1 + 0.07) – ^{5}

= 124,772

The offer is acceptable as PV of 5 years plan is offering excess amount than 3 years plan.

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