### 3.5 Compound Interest Formula

```3.5 Compound Interest Formula
• Imagine you deposit \$10,000 in a five-year cd.
The account pays 5.2% interested
compounded daily. How much will your
\$10,000 investment be worth by the end of
the 5 years?
Compound Interest Formula
r

B  p 1  
 n
n t
B = ending balance
p = principal
r = interest rate
n = number of compounds per year
t = time (in years)
Number of Compounds
• Annually
• n=1
• Semiannually
• n=2
• Quarterly
• n=4
• Daily
• n = 365 (or 366 in a leap year)
Marie deposits \$1,650 for three years at 3%
interest, compounded daily. What is her ending
balance?
n t
r

B  p 1  
 n
365  3
p = \$1,650 B  1,6501  0.03


365 
r = 0.03

n = 365
t=3
B  \$1,805.38
Kate deposits \$2,350 in an account that earns
interest at a rate of 3.1%, compounded monthly.
What is her ending balance after 5 years?
n t
r

B  p 1  
 n
12  5
p = \$2,350 B  2,3501  0.031


12 
r = 0.031

n = 12
t=5
B  \$2,743.45
3.5 Compound Interest Formula
APR vs. APY
• APR
– Annual interest rate
• APY
– Actual rate you earn with compounding interest
Ending Balance- StartingBalance
– To find APY:
StartingBalance
Sharon deposits \$8,000 in a one year CD at 3.2%
interest, compounded daily. What is Sharon’s
APY?
n t
\$8,260.13- \$8,000
r

APY
B  p 1  
\$8,000
 n
365  1
 0.032
B  8,0001 

APY  3.25%
365 

B  \$8,260.13
Barbara deposits \$3,000 in a one year CD at
4.1% interest, compounded daily. What is her
APY for the account?
n t
\$3,125.55- \$3,000
r

APY
B  p 1  
\$3,000
 n
365  1
 0.041
B  3,0001 

APY  4.19%
365 

B  \$3,125.55
```