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+(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+(0.075)/(4))^(4t) \\ (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) \\ (log1.62)/(log1.01875)=4t \\ 25.96986089=4t \\ t=(25.96986089)/(4) \\ t\approx6.49 \end{gathered}`

Hence, the required time is approximately 6.49 years