Problema Solution
$100 to invest at 8% per annum compound monthly, how long will it be before $150? If the compound is continuous, how long?
Answer provided by our tutors
P = $100
r = 0.08 or 8% annual rate
A = $150 the future value
- Compounded monthly
i = 0.08/12 = 0.04/3 interest rate per month
n = total number of months
A = P(1 + i)^n
150 = 100(1 + 0.04/3)^n
100(1 + 0.04/3)^n = 150
(1 + 0.04/3)^n = 150/100
n = log(1.5)/log(1 + 0.04/3)
by solving we find
n = 30.6 months
n = 2 years 6.6 months
n = 2.55 years
click here to see the step by step calculation
- Continuous compounding
t = the number of years
A = P*e^(r*t)
150 = 100e^(0.08t)
100e^(0.08t) = 150
t = (1/0.08)(ln(1.5))
t = 5.07 years