Question

You have $1,000 to invest in an account, and need to have $1,500 in one year. What interest rate would you need to have in order to reach this goal if the amount is compounded quarterly? Round your answer to the nearest percent.A) 9%B) 11%C) 5%D) 7%

Answer 1

Given:

You have $1,000 to invest in an account, and need to have $1,500 in one year.

Required:

What interest rate would you need to have in order to reach this goal if the amount is compounded quarterly?

Explanation:

The formula we need is

$\begin{gathered} r=n[(\frac{A}{P})^{\frac{1}{nt}}-1] \\ Where, \\ n(compounded) \\ A(Total) \\ P(Principal) \\ t(time) \end{gathered}$

Now,

$\begin{gathered} r=n[(\frac{A}{P})^{\frac{1}{nt}}-1] \\ r=4\times[(\frac{1500}{1000})^{\frac{1}{4\times1}}-1] \\ r=0.426728 \\ \text{ Then, convert r to R as a percentage} \\ R=r\times100 \\ R=0.426728\times100 \\ R=42.673\% \end{gathered}$