Question

Lionel invests $5500 today in a retirement account. He expects to earn 9.10 percent, compounded annually, on his money for the next 10 years. After that, he expects to earn 5 percent, compounded annually. How much money will he have in his account when he retires 25 years from now?

Answer 1

Given:

Invest amount = $5500

Rate = 9.10%

Time = 10 years

After that rate = 5%

Total time = 25 years

Find-:

The final amount after 25 years

Explanation-:

Future value is:

$FV=PV(1+r)^n$

Where,

$\begin{gathered} FV=\text{ Future value } \\ \\ PV=\text{ Present value} \\ \\ r=\text{ Rate} \\ \\ n=\text{ Time} \end{gathered}$

Amount after 10 years is:

$\begin{gathered} FV=PV(1+r)^n \\ \\ FV=5500(1+\frac{9.10}{100})^{10} \\ \\ FV=5500(1+0.091)^{10} \\ \\ FV=5500(1.091)^{10} \\ \\ FV=5500\times2.389 \\ \\ FV=13140.449 \end{gathered}$

The amount after 10 years is $13140.449

Amount after total years 25 then time for 5%

$\begin{gathered} \text{ Time}=25-10 \\ \\ \text{ Time}=15 \end{gathered}$

So, the amount is:

$\begin{gathered} FV=PV(1+r)^n \\ \\ FV=13140.449(1+\frac{5}{100})^{15} \\ \\ FV=13140.449(1+0.05)^{15} \\ \\ FV=13140.449(1.05)^{15} \\ \\ FV=13140.449\times2.079 \\ \\ FV=27318.0497 \end{gathered}$

The total amount after 25 years is $273178.0497