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 tn

n

r 1 p B

B = ending balancep = principalr = interest rate

n = number of compounds per yeart = 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?

tn

n

r 1 p B

p = $1,650r = 0.03n = 365t = 3

3 365

365

0.03 1 1,650 B

$1,805.38 B

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?

tn

n

r 1 p B

p = $2,350r = 0.031n = 12t = 5

5 12

12

0.031 1 2,350 B

$2,743.45 B

3.5 Compound Interest Formula

APR vs. APY

• APR– Annual interest rate

• APY– Actual rate you earn with compounding interest

– To find APY: Balance Starting

Balance Starting - Balance Ending

Sharon deposits $8,000 in a one year CD at 3.2% interest, compounded daily. What is Sharon’s APY?

tn

n

r 1 p B

1 365

365

0.032 1 8,000 B

$8,260.13 B

000,8$

$8,000 - $8,260.13 APY

3.25% APY

Barbara deposits $3,000 in a one year CD at 4.1% interest, compounded daily. What is her APY for the account?

tn

n

r 1 p B

1 365

365

0.041 1 3,000 B

$3,125.55 B

000,3$

$3,000 - $3,125.55 APY

4.19% APY