question 12\nkathy has $50,000 to invest today and would like to determine whether it is realistic for her…

question 12\nkathy has $50,000 to invest today and would like to determine whether it is realistic for her to achieve her goal of buying a home for $150,000 in 10 years. what return must she achieve in order to buy her home in 10 years?\na. above 10%\nb. between 8% to 10%\nc. exactly 10%\nd. below 8%\ne. none of the choices\n1.5 points

question 12\nkathy has $50,000 to invest today and would like to determine whether it is realistic for her to achieve her goal of buying a home for $150,000 in 10 years. what return must she achieve in order to buy her home in 10 years?\na. above 10%\nb. between 8% to 10%\nc. exactly 10%\nd. below 8%\ne. none of the choices\n1.5 points

Answer

Explanation:

Step1: Use compound - interest formula

The compound - interest formula is $A = P(1 + r)^n$, where $A$ is the future value, $P$ is the present value, $r$ is the annual interest rate, and $n$ is the number of years. We know that $P=$50000$, $A = $150000$, and $n = 10$. We need to solve for $r$. So, $150000=50000(1 + r)^{10}$.

Step2: Simplify the equation

Divide both sides of the equation by $50000$: $\frac{150000}{50000}=(1 + r)^{10}$, which simplifies to $3=(1 + r)^{10}$.

Step3: Solve for $r$

Take the 10 - th root of both sides: $1 + r=3^{\frac{1}{10}}$. $3^{\frac{1}{10}}\approx1.1161$. Then $r=3^{\frac{1}{10}}-1\approx0.1161 = 11.61%$.

Answer:

A. Above 10%