Question

A rich relative dios and you inherit $120,000. How much will you have for your retirement of age 60) if you invest the inheritance in an account paying 2.0% annual interest compounded monthlyassuming that you are 18 years old now?O A. 569,287,040,00OB. 5481,030.54O C. $287.040,00OD $1,700,400.00previow answors

Answer 1

To answer this question we will use the following formula for compounded monthly interest:

`A=A_0(1+(r)/(12))^(12t),`

where A₀ is the initial amount, r is the annual interest as a decimal number and 12 is the number of years.

Notice that:

`60-18=42.`

Therefore, substituting t=42, r=0.02, and A₀=120000 we get:

`A=120000(1+(0.02)/(12))^(12\cdot42)\text{.}`

Simplifying the above result we get:

`\begin{gathered} A=120000(1.001\bar{6})^(504) \\ \approx120000\cdot2.314747889 \\ \approx277769.75 \end{gathered}`

Answer: $277,769.75.