Exponentials and logarithms

Question

Lisa, a real estate agent, earned a Big commission for selling a house. If she puts the money into an account that earns 11.32% interest compounded continuously, how long will it take for her money to double? Round your answer to the nearest month.

Show work.

Answer 1

Continuously compounded interest rate the Principal amount grows according to the formula

P = P₀*e^r.t

where P0 is the Principal Amount invested. P is the resulting Principal after time t, at an interest rate r

To double the principle means

P = 2*P₀

You can use the equation above, take the logarithm of both sides of the equation and calculate t.

Answer 2

The equation to use is A = Pe^rt

P = initial investment

A = value of investment after t years

r = rate = 0.1132

t = number of years = unknown

If the investment doubles, then A = 2P

2P = Pe^0.1132t

2 = e^0.1132t

0.1132t = ln2

0.1132t = 0.693

t = 0.693/.1132

t = 6.12 years

t = 6 years + 0.12years

t = 6 years + 0.12(12) months

t = 6 years + 1 month