MATH SOLVE

3 months ago

Q:
# What interest rate, to the nearest tenth of a percent, that is required for an investment subject to continuous compounding to increase 150% in 5 years?

Accepted Solution

A:

Answer:It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.Step-by-step explanation:Use the formula for continuous compounding[tex]X(t) = Pe^{rt}[/tex]where r stands for the (annual) interest rate, t for time in years, P for the initial principal (investment) and X is the amount after t years. (this formula can be beautifully derived from just basic considerations, btw)We are given t=5, and percent increase on the initial P, so we can solve for r[tex]X(5) = 1.5P=Pe^{r\cdot5}\\1.5=e^{r\cdot5}\\\ln 1.5=\ln e ^{5r}\\\ln 1.5=5r\\r = \frac{\ln 1.5}{5}=0.081\rightarrow 8.1\%[/tex]It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.