Chapter 5-3 and 5-4

Hope everyone that went to prom/prom mania had a great time!!

Formulas:

1. A(t) = A0(1+r)^t - used when compounding
A0 - starting amount
r - rate
t - number of times compounded in given times span

2. A(t) = A0b^t/k - used when things are doubling, tripiling, halfing, ect
A0 - starting amount
b - doubling, tripiling, , ect
t - amount of time
k - how long it takes to double, triple, half, ect

3. Rule of 72 - to find how long it takes for something to double. Find 72/r
*r is not a decimal here

4. **Only use when compounding continuously
P(t) = P0e^rt
P0 - starting amount
e - on ln button
r - rate
t - time

Example 1: A bank advertizes that if you open a savings acconunt you can double your money in 12 years. If you invest $1,000, how much money will you have after 5 years?

You use formula 2 because its talking about double and thats the only formula that talks about doubling.
A = A0b^t/k
A(t) = 1,000(2)^5/12
= $1,334.84

Example 2: If $1,000 is invested in a savings account that is compounded monthly at .5% for 5 years how much money did you gain?
b. What if it was compounded continuously?

A(t) = A0(1+r)^t
t = 6 months
A(t) = 1,000(1+.005)^60 = $1,348.85
b. P(t) = P0e^rt
= 1,000e^(.005)60
= $1, 349.86

--Daniellee