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

I have to say 11%

A = P(1 + r/n)nt
A = 1,500.00(1 + 0.11/4)(4)(1)
A = 1,500.00(1 + 0.0275)(4)
A = $1,671.93

Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $1,500.00 at a rate of 11% per year compounded 4 times per year over 1 years is $1,671.93.

Answer 2

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?

Step-by-step explanation:

The formula we need is

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

Now,

`\begin{gathered} r=n[((A)/(P))^{(1)/(nt)}-1] \\ r=4*[((1500)/(1000))^{(1)/(4*1)}-1] \\ r=0.426728 \\ \text{ Then, convert r to R as a percentage} \\ R=r*100 \\ R=0.426728*100 \\ R=42.673\% \end{gathered}`