Question

Dan is 60 years old and plans to retire at age 70. He wants an extra $100,000 by the time he retires. He currently has $70,000 saved. If he invests this at 6% compounded monthly, how much will we have at the time he retires?

Answer 1

The formula for compounding interest monthly is shown as follows;

`A=P(1+(r)/(n))^(nt)`

Where the variables are;

`\begin{gathered} A=\text{amount at the end of the investment} \\ P=\text{amount initially invested} \\ r=annual\text{ rate of interest} \\ t=time\text{ in years} \\ n=\text{ number of compounding periods per year} \end{gathered}`

The amount after the period of investment shall be;

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=70000(1+(0.06)/(12))^(12*10) \\ A=70000(1+0.005)^(120) \\ A=70000(1.005)^(120) \\ A=70000*1.8193967340323313 \\ A=127357.7713822619 \\ A\approx127,357.77 \end{gathered}`

ANSWER:

By the time he retires at age 70 Dan would have $127,357.77

The correct answer is option B