Question

Your answer it t= ??? Years I need to know the years Enter the exact value or round to 2 decimals

Answer 1

In order to find the value of t, use the following formula for the amount obtained after a time t in compounded interest:

$A=P(1+\frac{r}{n})^{(nt)}$

where,

A: final amount = 8100

P: initial amount = 5000

n: times at year = 4 (quaterly)

t: time = ?

r: rate = 7.5% = 0.075

By replacing the previous values into the expression for A, we get:

$\begin{gathered} 8100=5000(1+\frac{0.075}{4})^{4t} \\ \frac{8100}{5000}=(1.01875)^{4t} \\ 1.62=(1.01875)^{4t} \end{gathered}$

Next, we apply log with base 1.01875 to cancel this base right side, as follow:

$\begin{gathered} log_{1.01875}1.62=log_{1.01875}(1.01875)^{4t} \\ \frac{log1.62}{log1.01875}=4t \\ 25.96986089=4t \\ t=\frac{25.96986089}{4} \\ t\approx6.49 \end{gathered}$

Hence, the required time is approximately 6.49 years