Formulas

1. A(t) = Aₒ(1 + r)^t ---> Used when compounding

Aₒ = starting amount r = rate

t = amount of time compound in given timespan

2. A(t) = Aₒb^t/k ---> Used when things are doubling, tripling, halfing, etc.

Aₒ = starting amount b = doubling(2), tripling(3), etc.

t = amount of time k = how long it takes to double, triple, etc.

3. Rule of 72 – to find how long it takes for something to double

72 ÷ r% r is not a decimal

4. P(t) = Pₒe^rt only used when compounding continuously

Pₒ = starting amount e = on ln button

r = rate t = time

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

A(t) = 1,000(2)^5/12 = $1,334.84

Ex 2. A radioactive substance has a half-life of 5 days. This means that half the substance decays in 5 days. At what rate does the substance decay each day?

A(t) = Aₒ(1/2)^t/5 Aₒ = (1/2)^1/5 · t Aₒ = (.87)^t

1 - r = .87 r = .13 = 13%

Ex 3. If $1,000 is invested in a savings account that is compounding monthly at .5% for 5 years how much money did you gain? What if it was compounding continuously?

A(t) = 1,000(1 + .005)^60 = $1,348.85 $348.85

P(t) = 1,000e^.005(60) = 1,000e^.3 = $1,349.85 $349.85