Pe^rt formula. Interest

1. Exponential Growth/Decay

2. Exponential Function
y = a • rt
a = original amount, r = rate t= time
Rate can be several things….
(1 ± %) for growth or decay
(2) For “double”
(1/2) for half life

3. 2) Change the following percent's to decimals:
a) 23% b) 10% c) 5% d) 6.25%

4. 2) Change the following percent's to decimals:
a) 23% b) 10% c) 5% d) 6.25%
.23 .10 .05 .0625

5. Rates use “1” to represent staying the same, so
• If something is growing by 3%, the rate is “1 + .03” or 1.03
• If something is shrinking by 5%, the rate is “1-.05” or .95

6. Continuously compounded interest
A= Pe rt
• Your bank is offering a savings account with a
nominal rate of 1.5%,compounded continuously. If
you deposit $1,000 in 2010, what will your balance
be in 2020?
P = principle (original amount) - $1000
R = rate - .015
T = time – 10 years
Not a variable….use the
NUMBER

7. Continuously compounded interest
A= Pe rt
• Your bank is offering a savings account with a nominal rate of
1.5%,compounded continuously. If you deposit $1,000 in 2010, what will
your balance be in 2020?
A = 1000e .015(10)
A = 1161.83

8. How long would it take a $500 investment to
double if the interest was compounded
continuously at 3%?

9. How long would it take a $500 investment to
double if the interest was compounded
continuously at 3%?
1000 = 500e .03t

10. How long would it take a $500 investment to
double if the interest was compounded
continuously at 3%?
1000 = 500e .03t
2 = e.03t Divide by 500
ln2 = lne .03t Add ln to each
side
ln2 = .03t lne Move the
exponent
.6931 = .03t Simplify the ln
t= 23.10 Divide by .03