Periodic Compound Interest. Annual Compound Interest.

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Presentation transcript:

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 = 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

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

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, r e, is the annual yield, use it like annual compounded interest ( m = 1). 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 n th root is used to cancel an n th power.

Determining the Yield Suppose an investment of $9000 matures to a value of $12000 over 4 years. Determine the effective rate, r e, The APY is about 7.457%

Determining the Yield If a bond purchased for $700 matures to a value of $1200 over 8 years, what is the effective rate, r e. The APY is about 6.97%