Time Value of Money Summary Sheet

Time Value of Money 1. There is time value attached to money which means that with the passage of time, the value of money decreases. It also means that a rupee today is worth less a year hence. The rate at which the value of money decreases is the discount rate. 2. We have learnt in school, the various concepts like simple interest, compound interest, principal, amount etc. 3. Simple interest means that the interest is calculated only on the principal amount whereas compound interest means the interest is calculated on both the principal and interest amounts. 4. Everyone is familiar with the formula for calculating amount when a sum of money is invested at a certain rate of interest, r for n period with interest compounded annually. A = P (1+r)n In financial language, we denote P= Present value; r = rate of interest ; n = number of years and A= future value 5. Using the above equation we can re write the equation as: FV = PV (1+r)n 6. Therefore, given the present value of a sum of money, the rate of interest and the number of periods, we can find the future value using the above formula. In order to make the calculations easier, the value of the term (1+r) n can be founding using the PVIF (r%, n) table . So, in order to find out the future value of a single sum of money, one can use the formula, FV = PV X FVIF (r%,n)

7. From equation 5, we can also find the present value of a given future sum at a discount rate r, for n period. PV = FV /(1+r)n In order to make calculations easier, one can find the value of the term (1/(1+r)n) using the PVIF (r%, n) tables. So, in order to find out the present value of a single sum of money, one can use the formula, PV = FV X PVIF (r%, n) 8. When we invest or receive equal sums of amount at equidistant periods of time, it is known as an annuity. There are two types of annuities: a. Ordinary Annuity: When the amounts are received /paid at the end of the period.

b. Annuity due: When the amounts are received/paid at the beginning of the period. 9. When equal sums of amounts are deposited at equidistant periods of time, the amount accumulated at the end of the period is called Future Value of An Annuity (FVA). This can be found out using the formula, FVA = Annuity X FVIFA (r%, n) 10. When equal sums of amounts are to be received/paid at equidistant periods of time in the future, in order to find the present value of such amounts, we use the formula, PVA = Annuity X PVIFA (r%,n) 11. We use time value of money in various applications like financial planning, capital budgeting etc. 12. While solving a Time Value for money problem, it is important to follow the following steps: i) Read the problem carefully in order to identify and list all the given values ii) Identify whether you have to calculate the Present Value of a sum of money, Future Value of a sum of money, Present Value of an Annuity or Future Value of an annuity. iii) Having identified the above, proceed to the calculations. iv) Remember, it is always advisable to use a time line in order to know the position of the cash flows. Please find below some solved problems.

Practice Problems

1. If you deposit Rs.3,000 today at 8 percent rate of interest in how many years (roughly) will this amount grow to Rs.1,92,000 ? Work this problem using the rule of 72–do not use tables. ( 54 years) 2. You can save Rs.5,000 a year for 3 years, and Rs.7,000 a year for 7 years thereafter. What will these savings cumulate to at the end of 10 years, if the rate of interest is 8 percent? (Rs. 90, 281) 3. Krishna saves Rs.24,000 a year for 5 years, and Rs.30,000 a year for 15 years thereafter. If the rate of interest is 9 percent compounded annually, what will be the value of his savings at the end of 20 years? (Rs. 14,04,010) 4. You plan to go abroad for higher studies after working for the next five years and understand that an amount of Rs.2,000,000 will be needed for this purpose at that time. You have decided to accumulate this amount by investing a fixed amount at the end of each year in a safe scheme offering a rate of interest at 10 percent. What amount should you invest every year to achieve the target amount? ( Rs. 3,27,600) 5. A finance company advertises that it will pay a lump sum of Rs.100,000 at the end of 5 years to investors who deposit annually Rs.12,000. What interest rate is implicit in this offer? (26%) 6. Someone promises to give you Rs.5,000,000 after 6 years in exchange for Rs.2,000,000 today. What interest rate is implicit in this offer? (16.49%) 7. At the time of his retirement, Rahul is given a choice between two alternatives: (a) an annual pension of Rs120,000 as long as he lives, and (b) a lump sum amount of Rs.1,000,000. If Rahul expects to live for 20 years and the interest rate is expected to be 10 percent throughout , which option appears more attractive?