**6.1. Definition of Time Value of Money**

Money certainly has value; but the value of money today is not the same as the value for tomorrow. This year you may have KES10,000, but next year the same money will have less value. This difference is not due to the passage of time per se, but the changing economic situations with time. The difference in the value of money between the present and the future is referred to as the time value of money (TVM).

The time value of money is a concept in financial management which suggests that money in the present is worth more than the same amount of money in the future. This concept is based on the fact that money today can be invested to earn more returns in the future.

Assume that someone wants to give you KES120,000 today or spread it over the next 12 months with payments of KES10,000 per month. Which option do you take? Based on the time value of money, the KES120,000 today is better because you can invest in it to generate more income. Furthermore, if you spend the money today, you buy more items than you can buy with the same money next year because items will become more expensive over time.

The concept of time value of money is important to learn because it helps a person to decide what they can do with their money. You can decide which job pays better by looking at time value of money and the frequency of the payments they make. Time value of money is also used to choose investment options among various alternatives. Once an individual invests their money in an asset, their investment grows over time. Whether you choose a savings account, bond, or mutual funds, the money will grow through compounded interest earned. However, money that is kept without any investment will lose value. Thus, it makes little sense to keep your money in cash because it will lose value in the future.

Inflation erodes the value of money, and reduces the purchasing power of a consumer. If someone keeps money in cash, they may not be able to buy enough goods when inflation hits the economy. For instance, if you had KES 10,000 to buy fuel last year when the prices were KES100 per litre, you could buy 100 litres of fuel at the time. If the price rises to KES200 this year, you can only be able to buy 50 litres of fuel this year.

Inflation and purchasing power must be factored in when you invest money because to calculate your real return on an investment, you must subtract the rate of inflation from whatever percentage return you earn on your money.

** 6.2. Importance of Time Value of Money**

Time Value of Money (TVM) is an important concept in finance because it provides the foundation for investment and consumption decisions. It is helpful in various aspects of finance, from negotiating a salary, making purchase decisions, to choosing an investment project. TVM enables individuals and organizations to evaluate various investment options and make the best financial decisions. This concept helps us understand the difference between the present value and future value of our money. Time value of money is important in the following ways:

: TVM is used to calculate the present value of interest earned on investment as well as on the interest itself. Compounding interest occurs when an investment or savings earn interest, and then the same interest earns more interest in subsequent years. In this regard, an investment can earn interest on the principal amount and all interest from previous years. Interest on interest has a compounding effect on money. For example, if you have KES 100 and save in an interest earning account with 10% interest, you get KES 110 in the second year. For the third year, your interest will be 10% of KES 110 instead of KES100.*Compounding Interest*: The concept of present value of money is important when making decisions in financial management because managers need to understand the present value of the benefits of a particular decision and compare them with the opportunity costs of other alternative decisions.*Financial Management*: A company can decide to put their funds in a particular investment that earns interest, but they must consider the opportunity costs of foregoing other investment options. It is important to choose an investment that earns higher net present value from future expected cash flows.*Capital Budgeting*: Another importance of time value of money is that it helps individuals to make informed personal finance decisions. Individuals can use their knowledge in TVM to make financial decisions and achieve their financial goals. An individual can also use TVM to evaluate two or more investment options. For example, a company may provide interest on savings such that if you deposit $8,000 today, you will get 8,800 after one year. This investment option looks good because you get $800 on top of what you saved. However, you need the time value of money concept to help you decide whether this savings option is really good for you. If the present value of the future amount you expect is less than the current amount you have, then that investment is not worth it.*Personal Finance Decisions*: The TVM concept is important for making investment decisions. When deciding to invest, one needs to consider several factors including opportunity cost, risk, and inflation. Prices of goods rise over time due to inflation, so the amount of money one has today is worth much more than the same amount in the future. Therefore, it is important to invest money owned now instead of letting them stay idle in the bank. But then, investors must consider alternative investment options that give more returns.*Investing and Inflation*

**6.3. Future Value of Money**

The future value of money is the value of a certain amount of money at some point in the future. For example, you may be told to find the future value of $2,000 in the next 5 years. Based on what we have learned about the time value of money, an amount of $2,000 will be worth less than that after five years. Investors need to calculate the future value of their potential investments in order to make a good decision.

*How to Calculate the Future Value of Money*

The formula used to calculate the future value of money is:

** FV = PV (1+i)^{n}**; where:

- PV is the amount of money in the current period
- i = assumed interest rate or discounting rate; and
- n = number of years

Assumed interest rate x is the rate at which all future cash flows of an investment is discounted to get the present value. It is the rate of return that investors expect from their investments. A discount rate is also about how much money loses value annually, or how much money you would earn from investing your money. For example, if the discounting rate is 10%, it means that if you invest your money you will get returns of 10% every year. If you don’t invest the money, it will lose value at the rate of 10% per year.

For example, Mrs. Karanja has $3,000 today in her bank account where she earns an annual interest rate of 5.5%, what will be the future value of her savings after 15 years?

Using the formula of future value above, Mrs. Karanja’s money will be calculated as follows:

FV = $3,000 × (1+0.055)^{15} = *$6,697.*

Therefore, based on an annual interest rate of 5.5%, Mrs. Karanja’s money will be worth $6,697 in the next fifteen years. Is it worth making such an investment?

**6.4. The Present Value of Money**

Assuming you have $10,000 in your bank account today. Of course that is the present value of your money because it is exactly the amount you can spend at present. However, if you expect to be paid $10,000 in the next 1 year, the present value would be less than that. The present value of the future $10,000 is the amount that you need to invest today to receive $10,000 after one year.

Based on the illustration above, the present value of money refers to the current value of money that we expect to receive in future. In technical terms, the present value can be defined as the amount of money that is obtained by discounting the future value of cash flows. A discounting rate is the interest rate applied to future cash flows to determine their present value. It is used when appraising an investment project to determine whether it is viable or not.

*How to Calculate the Present Value of Money*

The present value of money is calculated using the future value; but the formula is the in the reverse. The PV is calculated by applying a discounting rate on the future cash flows or future payments. Essentially, you need to rearrange the formula for the future value by dividing rather than multiplying as shown below:

PV= FV/(1+i)^{n}

Where:

- PV = Present value (original amount of money)
- FV = Future value
- i = Interest rate per period
- n = Number of periods

Alternatively, the PV formula can be rearranged as follows:

PV = FV × (1+i)^{-n}

For example, assume Mrs. Karanja expects to earn $40,000 as her retirement benefits after 15 years. Using a discounting rate of 5.5%, calculate the amount of money she needs to save today for her retirement.

PV = 40,000 × (1+0.055)^{-15} = *17,917.*

In this regard, Mrs. Karanja needs to have a present value of $17,917 to put into a savings plan earning 5.5% over the next 15 years to get a future payment of $40,000.

**6.5. Loan Amortization**

Loan amortization refers to the process of scheduling out a fixed rate loan into equal payments. This allows a borrower to pay loans for equal amounts or installments every month or every year. A portion of the amortized loan or installment goes towards the payment of interest while the other portion pays the principal loan amount. Lenders use loan amortization schedules to determine the amount of monthly payments that borrowers are required to pay. The loan amortization schedule also provides repayment details for customers. Borrowers can also use the amortization schedule to establish the amount of debt that they can afford, and how much they can save.

An amortization schedule is a table that has the periodic payments. It shows the amount of the loan that goes towards the principal and the amount that covers interest. In the early stages of the schedule, majority of the installment amounts go towards interest. However, towards the end of the loan amortization schedule a large amount of the money paid each period goes to the remaining loan principal. In this regard, the percentage of each instalment that goes towards interest diminishes with time, while the percentage that goes toward the principal increases.

For example, a loan amortization schedule for fixed-rate mortgage loan of $165,000 lasting for 30 years at an interest rate of 4.5% can be amortized using the amortization schedule below:

Apart from mortgage loans, car loans and personal loans can also be amortized over a set period of time with monthly payments.

**Calculation of a Loan Amortization**

Borrowers and lenders use amortization schedules for installment loans that have payoff dates that are known at the time the loan is taken out, such as a mortgage or a car loan. Most formulas used to calculate loan amortization schedule is built into a software and customized for each borrower. Loan amortization can be calculated if the term of the loan and total periodic payments are known. The formula to calculate the monthly principal due on an amortized loan is as follows:

** Principal Payment** = Total Monthly Payment – [Outstanding Loan Balance x (Interest Rate / 12 Months)].

For example, a home owner took a mortgage of $250,000 that has 30-year term, an interest rate of 4.5% and monthly installments of $1,266.71. For the first month, the loan is amortized as follows:

Principal Payment = 1,266.71 – [250,000 x (0.045/12)] = **$ 329.21**

The interest and principal payment for the second month is calculated by first subtracting the principal payment from the loan balance ($250,000-$329.21). This gives a new loan balance of $249,670.79. Using the new loan balance, you repeat the calculation you did for the first month, and then do the same for all the subsequent months.

The total monthly payment is calculated using the formula below:

*Total Monthly Payment **= Loan Amount [ i (1+i) ^ n / ((1+i) ^ n) – 1) ]*

Where; i = monthly interest rate, n = number of payments over the loan’s lifetime.

Monthly interest is given by the annual interest rate divided by 12 months; while the number of payments is calculated by multiplying the number of years of the loan term by 12 months. Therefore, for a 30-year loan of $250,000 with an interest rate of 4.5% as shown in the example above, the monthly payments are calculated as follows:

** Total Monthly Payment** = $250,000 [(0.00375 (1.00375) ^ 360) / ((1.00375) ^ 360) – 1)] = $1,266.71.

This is the total monthly payment due on the loan, including the sum of principal and interest amounts.