periodic compound interest. annual compound interest

Periodic Compound Interest

Annual Compound Interest

With interest for 1 year...

With interest for 2 years...

With interest for 3 years...

And so on...

Exponential Growth

Annual Interest

Example

P =

n =

i =

24000

What values are given?

8

7/100 = 0.07

Calculate the new balance

Try Another

12%, compounded quarterly

Consider interest on our $10000 over a one-year period, but now compounded quarterly.

Say the 12% is split into quarters so that 3% of interest is earned each quarter. Let i = interest per period = 0.12/4 = 0.03 n = number of times interest is computed = 4

Using the same compound interest formula, the new balance is computed to be

410000(1 0.03) 11255.09A

12%, compounded monthly

Consider interest on our $10000 over a one-year period, but now compounded monthly.

Say the 12% is divided so that 1% of interest is earned each month. Let i = interest per period = 0.12/12 = 0.01 n = number of times interest is computed = 12

Using the same compound interest formula, the new balance is computed to be

1210000(1 0.01) 11268.25A

Compound Interest Formula:

More frequent is better !

Keeps getting better !

Another Example

Avoid rounding errors !

Yet Another Example

A Different Question?

The “Present Value”

Another Example

Comparing Interest Rates

Growth in 1 year?

Effectively, 9.6%

Also, called the annual percentage yield (APY).The interest is equivalent to earning 9.6% annually.

Effectively, 9.74%

This account has an effective rate, or APY, of 9.74%

Effective Rate Formula

Compare Accounts

Annual Yield

Since the effective rate, re, is the annual yield, use it like annual compounded interest ( m = 1).

(1 )teA P r

If a deposit of $8000 earns interest with an APY of 6.8%, what is the value of the account at the end of 5 years?

Note an nth root is used to cancel an nth power.

Determining the Yield

Suppose an investment of $9000 matures to a value of $12000 over 4 years. Determine the effective rate, re,

412000 9000(1 )er

The APY is about 7.457%

412000

19000 er

Determining the Yield

If a bond purchased for $700 matures to a value of $1200 over 8 years, what is the effective rate, re.

81200 700(1 )er

The APY is about 6.97%