13.1 The Time Value of Money
Simple Interest I is calculated only on the principal
(amount borrowed) and is given by I = Prt where
P = principal
r = annual interest rate
t = time (in years)
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Time Value of Money: Simple and Compound Interest, Present and Future Value, Inflation, Study notes of Finance
The concepts of simple and compound interest, present and future value, and inflation. It includes formulas and examples for calculating simple interest, future value of simple interest loans, compound interest, and future value of compound interest. It also explains the concept of inflation and how it affects the value of money over time.
What you will learn
- What is the formula for calculating simple interest?
- What is the formula for calculating compound interest?
- How is the future value of a compound interest loan calculated?
- How is the future value of a simple interest loan calculated?
- What is inflation and how does it affect the value of money?
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13.1 The Time Value of Money
Simple Interest I is calculated only on the principal (amount borrowed) and is given by I = Prt where
P = principal
r = annual interest rate
t = time (in years)
Example. Find the simple interest paid to borrow $ for 6 months at 7%.
Future Value for Simple Interest
The future value of a simple interest loan, denoted A , is given by A = P (1 + rt ).
Example. Find the future value of $4800 in 6 months, if the annual interest rate is 7%.
Compound Interest ( calculated on principal plus any previously earned interest).
Future Value for Compound Interest is given by
𝑨 = 𝑷 (𝟏 +
𝒎 = 𝑷 (𝟏 +
𝒏𝒕
P = principal
r = annual interest rate
n = number of compounding periods per year
m = total number of compounding periods = nt
Example. What amount must be deposited today, at 5% compounded monthly, so that it will be $18,000 in 20 years?
The future value , A, of an amount that grows using continuous compounding is given by 𝐴 = 𝑃𝑒𝑟𝑡, where
P = principal
r = annual interest rate
t = time (in years)
e ≈ 2.71828183 is Euler's number.
Your calculator knows the value of e ; it’s easiest to use the ex^ button on your calculator when working with e.
Example. Suppose that a cup of your favorite coffee is $2.25. If the inflation rate persists at 2% over time, find the approximate cost of the coffee in 25 years.