Question

Explain the concept of the Time-Value-of-Money and provide an example. If you won the lottery and had a choice between taking a lump-sum payment today or a 10 year annuity, how would the TVM help you in making this decision? What information would you need to make a decision?

Answer 1

Time-value of moneysimply means that cash in hand today is worth more than the same amount of cash in the future.

The time value of money is the idea that there is greater benefit to receiving a sum of money now rather than an identical sum later

The formula for computing time value of money considers the payment now, the future value, the interest rate, and the time frame.

• FV = Future value of money
• PV = Present value of money
• i = interest rate
• n = number of compounding periods per year
• t = number of years

Based on these variables, the formula for TVM is:

FV = PV x [ 1 + (i / n) ] ^{(n x t)}

Eg:

Assume a sum of $100 is invested for one year at 20% interest. The future value of that money is:

100(1+0.02)¹=120

interpretation: 100$ payment now or 120$ after 1 year will have the same value if the interest rate is 20% p.a. compounded anually.

If you won the lottery and had a choice between taking a lump-sum payment today or a 10 year annuity, TVM would help you in making this decision as follows:

Determine the interest and then calculate the PV of the annuity taking N as 10

Compare the PV of annuity and the lumpsum lottery amount and then select that option which provides a higher PV.