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 inorder 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

Explanation

We are asked to find the interest rate that will yield $1500 for a sum of $1000 invested quarterly

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

In our case, we have

`\begin{gathered} P=\text{ principal=1000} \\ A=final\text{ amount=}1500 \\ n=number\text{ of times compounded yearly=}4 \\ t=1 \end{gathered}`

Thus, we will have

`\begin{gathered} 1500=1000(1+(r)/(4))^(4(1)) \\ \\ (1500)/(1000)=(1+0.25r)^4 \\ \\ 1.5=(1+0.25r)^4 \end{gathered}`

Solving for r

we will have

`r=0.42672,\:r=-8.4267`

Since the value increased, the rate will be positive

Therefore

`\begin{gathered} The\text{ rate will be 0.42672} \\ 42.67\text{ \%} \end{gathered}`

To the nearest per cent, we will have the annual rate as 42.7 %