Question

How long does it take for an investment of $4,800 to increase to $12,000 if it is invested at 8% per year compounded continuously? Round to the nearest tenth of a year

Answer 1

Answer;

11.9 years

Explanations:

The formula for calculating the compound amount is expressed as:

$A=P(1+r)^t$

where:

• P is the ,amount invested

,

• r is the r,ate

,

• t is the ,time taken

Given the following parameters

P = $4,800

A = $12,000

r = 8% = 0.08

Substitute

$\begin{gathered} 12,000=4800(1+0.08)^t \\ \frac{12000}{4800}=1.08^t \\ 2.5=1.08^t \\ ln2.5=tln(1.08) \\ t=\frac{ln2.5}{ln1.08} \end{gathered}$

Simplify to determine the value of t

$\begin{gathered} t=\frac{0.9163}{0.07696} \\ t\approx11.9years \end{gathered}$

Hence the time it will take for an investment of $4,800 to increase to $12,000 if it is invested at 8% per year compounded continuously is 11.9 years