Saving and Interest

February 2014

Saving and Interest

• An Equation to define Savings: – SAVING = Disposable Income – Consumption.

• Interest: – Simple Interest = The annual interest paid on the

initial amount saved. – Compound Interest = The interest paid on both

the initial principal amount AND the interest added to the principal.

Interest earned on an initial $100 saved at 8% interest

Year Simple interest adds

Total saving using simple interest

Compound interest adds

Total Savings using compound interest

1 $8.00 $108.00 $8.00 $108.00

2 $8.00 $116.00 $9.00 $117.00

3 $8.00 $124.00 $9.00 $126.00

4 $8.00 $132.00 $10.00 $136.00

5 $8.00 $140.00 $11.00 $147.00

6 $8.00 $148.00 $12.00 $159.00

7 $8.00 $156.00 $12.00 $171.00

8 $8.00 $164.00 $14.00 $185.00

9 $8.00 $172.00 $15.00 $200.00

Compound Interest Example• Simple interest: Is interest paid on the initial principal amount at a given rate

for a specified time. – I = P x R x T

• Compound interest: Is interest that is paid on both the principal and also on any interest from past years. For example, if you received 15% interest on a $1000 investment, the first year and reinvested the money back into the original investment, then in the second year, you would get 15% interest on $1000 and the $150 I reinvested. Over time, compound interest will make much more money than simple interest. The formula used to calculate compound interest is:– M = P( 1 + i )n

• M is the final amount including the principal.• P is the principal amount.• i is the rate of interest per year.• n is the number of years invested.

– Applying the Formula• Let's say that you have $1000.00 to invest for 3 years at rate of 5% compound interest.• M = 1000 (1 + 0.05)3 = $1157.62.• You can see that the $1000.00 is worth $1157.62.

The Rule of 72

• The rule of 72 is a simple way to illustrate the magic of compound interest

• Rule of 72– 72 divided by the rate of interest = the number of

years it will take for a saved amount to double when interest is allowed to compound.

– Example: Compound interest at 8% for 9 years• 72/8 = 9• At the end of 9 years the initial amount saved of $100

has doubled to $200. (see table).