School

Northeastern UniversityDepartment

Finance & InsuranceCourse Code

FINA 2201Professor

Ma LinlinChapter

5This

**preview**shows pages 1-2. to view the full**7 pages of the document.**FINA 2201 Chapter 5: Time Value of Money

1

Timeline: An important tool used in time value analysis; it is a graphical representation used to show the timing of cash

flows.

Future Value (FV): The amount to which a cash flow or series of cash flows will grow over a given period of time when

compounded at a given interest rate.

Present Value (PV): The value today of a future cash flow or series of cash

flows.

Simple Interest: Occurs when interest is not earned on interest.

Compounding: The arithmetic processof determining the final value of a cash flow or series of cash flows when

compound interest is applied.

Compound Interest: Occurs when interest is earned on prior periods’ interest.

Future Value

• You plan to deposit $100 in a bank that pays a 5% interest each year. How

much would you have at the end of Year 3?

• Finding the FV of a cash flow or series of cash flows is called compounding.

Step by step approach:

Formula approach:

• Notice that we multiple (1+I) at the beginning of each period

• We multiply (1+I) three times

Financial calculator

Requires 4 inputs into calculator, and will solve for the fifth.

Financial Calculators

N = Number of periods. Some calculators use n

rather than N.

I/R = Interest rate per period. Some calculators

use i or I rather than I/YR.

PV = Present value. In our example, we begin

by making a deposit, which is an outflow; so the

PV should be entered with a negative sign. On

most calculators, you must enter the 100, then

press the þ/− key to switch from þ100 to −100.

If you enter −100 directly, 100 will be subtracted

from the last number in the calculator, giving

you an incorrect answer.

PMT = Payment. This key is used when we

have a series of equal, or constant, payments.

Because there are no such payments in our

illustrative problem, we enter PMT 1⁄4 0. We will

use the PMT key when we discuss annuities

later in this chapter.

FV = Future value. In this example, the FV is

positive because we entered the PV as a

negative number. If we had entered the 100 as

a positive number, the FV would have been

negative.

$1 today is worth more than a dollar in the

future because Money has time value

FVn = PV(1+i) FV3 = PV(1+i)3 = $100(1.05)3 = $115.76

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FINA 2201 Chapter 5: Time Value of Money

2

Opportunity Cost: The rate of return you could earn on an alternative investment of similar risk.

Present value

Discounting: The process of finding the present value of a cash flow or a series of cash flows; discounting is the reverse of

compounding.

• You plan to have $115.76 in your bank account at the end of Year 3, if the interest rate is 5%, how much you should

deposit today?

• Finding the Present Value (PV) of a cash flow or series of cash flows is called discounting (the reverse of

compounding).

Step by step approach

Formula approach:

Financial Calculator

• What annual interest rate would cause $100 to grow to $125.97 in 3 years?

• If the interest rate is 20% per year, how long before one dollar to double?

PVn = PV(!+t)n Present Value = FVn

(PV) (1+ i)n

PV = FVN /(1 + I)N= FV3 /(1 + I)3

= $115.76/(1.05)3

= $100

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