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## 6.3 Simple Interest

PLEASE NOTE: This book is currently in draft form; material is not final.

### Learning Objectives

1. Define simple interest.
2. Calculate simple interest for an investment.

What do you think should happen if Mary wishes to borrow the \$9 from Martha for two weeks? Should she assume she’ll only have to pay the same \$5 of interest? Of course not! It is likely to expect that Martha will desire more interest to compensate her for the opportunity cost of the second week. So it is always important to note for what period an interest rate applies! For example, it’s no use using a 2-year interest rate if you need a 1-week rate!

Let’s assume that Martha is willing to lend to Mary for the second week for an additional \$5; determining interest in each period from outstanding principal only is known as simple interestDetermining interest in each period from outstanding principal only.. Two weeks of borrowing means (2 × \$5) = \$10 of interest owed, for a final payment of (principal + interest) = (\$9 + \$10) = \$19.

Equation 6.2 Simple Interest for 2 Periods

principal + first week’s interest + second week’s interest = FV
PV + (PV × r) + (PV × r) = FV PV × (1 + r + r) = FV PV × (1 + 2r) = FV

The total interest paid is \$10 vs. \$9 borrowed, so the implied 2-week interest rate is (\$10/\$9) = 111.11%. Note that this is precisely twice the 1-week rate of 55.56%. To generalize for more periods, since the interest paid will be the same for each period, we can simply multiply the interest rate by the number of periods, n, to get the effective rate for that period.

Equation 6.3 Simple Interest for n Periods

PV × (1 + nr) = FV

### Key Takeaway

• Simple Interest: PV × (1 + nr) = FV

### Exercises

1. If \$300 is invested at a 4% interest rate, how much simple interest will be earned in 4 years? What is the total FV of the investment?
2. If a loan shark offers to give you \$5,000 today in return for \$8,000 in three weeks, what is the implied weekly interest rate assuming simple interest?
3. A bank account currently has a balance of \$720 dollars. If the initial deposit was made four years ago, and the simple interest rate is 5%, what was the initial deposit?