Problema Solution
If an amount of $10,000 is invested at continuous compounding, what rate of interest is necessary for the $10,000 to grow to $100,000 in 25 years
Answer provided by our tutors
P = $10,000 principal amount (initial investment)
r = annual interest rate (as a decimal)
t = 25 number of years
A = $100,000 amount after time t
A = Pe^(r*t)
e^(r*t) = A/P
r = (1/t) ln(A/P)
r = (1/25) ln(100,000/10,000)
r = (1/25) ln(10)
r = 0.0921 or 9.21%
9.21% annual rate of interest is needed.