Unit 2 – Time Value of Money

## *Lesson 2.6: Time Value of Money in Practice*

In the previous five Lessons we have explained what the Time Value of Money (TVM) is all about and went further to explain each component which make up the TVM Calculations. In this Lesson, we will be focusing on providing you with examples that highlight when it is appropriate to use the TVM Calculations to find each one of the five components.

As a review, the five components that make up the TVM Calculation are as follows:

- Present Value (PV)
- Number of Payments or Compounding Periods (N)
- Annual Nominal Interest Rate (I/Y)
- Amount of Periodic Payment (PMT)
- Future Value (FV)

**Determine Present Value of Periodic Payment Stream – Solve for PV**What is the PV of periodic payment stream that provides you with $5,000 at the end of each year for the next five years, with an assumed interest rate of 8%, compounded annually?

In this scenario, this is the information we know:

Number of Compounding PeriodsN

5 (5 years)

Annual Nominal Interest Rate

I/Y

8% or 0.08 (compounded annually)

Amount of Periodic Payment

PMT

$5,000 (at end of each year)

Future Value

FV

$0 (nothing left over after 5 years)

__Solve for Present Value (PV):__

Using the TVM Calculation, we can determine that the Present Value of the example above is $19,963.55. This income stream is worth $19,963.55 in today’s dollars.**Determine How Long You Have to Save – Solve for N**How long will you have to save in order to have $350,000, considering that you currently have $50,000, and are investing an extra $500 at the beginning of every month, with an assumed rate-of-return of 4%, compounded monthly?

Present ValuePV

$50,000

Annual Nominal Interest Rate

I/Y

4% or 0.04 (compounded monthly)

Amount of Periodic Payment

PMT

$500 (saved at the beginning of every month)

Future Value

FV

$350,000

__Solve for Time (N):__

Using the TVM Calculation, we can determine that the Number of Compounding Periods of the example above is 274.9 months, which divided by 12, gives us 22.91 years**Determine Interest Rate Needed for Savings Plan – Solve for I/Y**What rate-of-return (interest rate) will you need to save up for a down payment on a property if you already have $75,000 ready to invest, are saving an additional $700 at the beginning of every month, for the next 8 years. You will need a total of $225,000 for your down payment.

Present ValuePV

$75,000

Number of Compounding Periods

N

96 months (8 years x 12)

Amount of Periodic Payment

PMT

$700 (saved at the beginning of every month)

Future Value

FV

$225,000

__Solve for Interest Rate (I/Y):__

Using the TVM Calculation, we can determine that the required Rate-of-Return (or Interest Rate) is 7.25% per year, compounded monthly.**Determine Loan Payment Amount – Solve for PMT**As a means to purchase a car worth $25,000, you decide to get a bank loan. The loan offers an interest rate of 4.2% per year, compounded monthly. Your loan agreement states that you will need to pay off the loan in 6 years’ time, at which point you will no longer owe any more money. What is the monthly payment you will need to make in order to satisfy the terms of this loan?

Present ValuePV

-$25,000

Number of Compounding Periods

N

72 months (6 years x 12)

Annual Nominal Interest Rate

I/Y

4.2% or 0.042 (compounded monthly)

Future Value

FV

$0 (Loan is fully paid off at end of term)

__Solve for Periodic Payment (PMT):__

Using the TVM Calculation, we can determine that you will have to make a Monthly Loan Payment of $392.04, at the beginning of every month.**Determine the FV of a Periodic Savings Plan – Solve for FV**You are looking to retire in 7 years. You have already saved $337,000 over the course of your working years, but you will also be making $10,000 lump-sum deposits to your retirement account at the beginning of every year. The investments that you are holding will produce a Rate-of-Return of 5.5% during this time. How much money will you have in your account when you retire?

Present ValuePV

$337,000

Number of Compounding Periods

N

7 Years

Annual Nominal Interest Rate

I/Y

5.5% or 0.055 (compounded annually)

Amount of Periodic Payment

PMT

$10,000 (at the beginning of every year)

__Solve for Future Value (FV):__

Using the TVM Calculation, at the end of the 7 years, you will have $577,442.61 in your retirement account.

**Summary**

As you can see from the examples, the TVM Calculations can offer you much support when building a framework behind your financial planning, help you weigh options regarding money, and identify whether goals and objectives are fitting for you based on your situation and financial circumstances.

Obviously, these calculations rely on making assumptions, and as we know, only some of our financial situations are established with pre-determined and guaranteed terms (like those of a loan). For others, such as retirement savings, the actual results could vary depending on factors such as a varying rate-of-return (or interest rate) or changes to your monthly savings. In these circumstances, the TVM Calculations act as an initial framework, but must be revised and recalculated periodically to ensure that you remain on track to accomplish your goals and objectives. Due to this, the TVM only makes up a portion of the work that is done by a financial planner. It is a tool that can be used but should only be one factor that influences an individual’s financial decisions.

Meeting with a financial planning professional may seem daunting as much of what you might discuss may not be familiar topics for you. We hope this Unit on the Time Value of Money has provided you with the confidence to deal with any financial planning requirements that you may have been delaying.