Compound interest

1
Compound interest

• Section 5.6

2
Compound interest Deposit P dollars in account at
beginning of time. Account earns interest, then
interest is added to account balance. Next time
the interest is calculated, you earn interest,
not only on the original amount deposited, but
also on previous interest.
P principal (present value, initial deposit,
amount invested) A amount after t years r
annual interest rate (decimal form) n number
of times it compounds per year t number of
years
3

• expl 4
• Find amount in account after a period of 1.5
  years if 300 is invested at 12 compounded
  monthly.

12 r .12
compounded monthly
n 12
t 1.5 years
investing P 300
4

• expl 16
• Find the present value (principal) needed to
  earn 300 after four years at 3 compounded
  daily.

compounded daily
t 4, A 300, r .03
n 365
Round intermediate answers to 4 decimal places.
5

• Continuously compounding
• Instead of compounding every month, day, etc,
  pretend the interest compounds every second, or
  even quicker than that.

where P principal A amount in account after
t years r annual interest rate t number of
years
6
expl 10 Find amount in account after a period
of 3 ¾ years if we invest 100 at 12 compounded
continuously.
P 100, r .12, t 3.75
7

• expl 34
• How many years will it take for an initial
  deposit of 25,000 to grow to 80,000? Assume a
  rate of interest of 7 compounded continuously.

Divide by 25000
Variable in exponent
x ay y loga x
(in years)
8

• expl
• Bob invests 1000 into an account paying 5
  compounded semiannually. How long must he wait
  until he has 5000?

compounded semiannually
n 2
P 1000, A 5000, r .05, t ?
Variable in exponent
9
So take natural log of both sides to undo the
exponential function.
Round intermediate answers to 4 decimal places.
(in years)

• 5.6 homework 1, 3, 9, 11, 15, 17, 33, 36, 45,
  51, 53, 54