periodic compound interest. annual compound interest
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 =
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%