Question

Kathy 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 with this investment. What return must she achieve in order to buy her home in 10 years?

a) About 12%
b) About 13%
c) About 9%
d) About 10%

Answer 1

Answer:

a) About 12%

Step-by-step explanation:

We need to find the interest rate required to achieve her goal, so we will need to use the interest-compound formula:

$FV=PV(1+i)^{n}$

Where:

PV= Present Value

i= interest rate

FV= Future Value

n= number of periods

replacing the data provided:

$150.000=50.000(1+i)^{10}$

solving for i:

first, divide both sides by 50.000 to simplify the equation:

$3=(1+i)^{10}$

Take $10^{th}$ roots of both sides:

$1+i=$±$\sqrt[10]{3}$

solve for i:

$i=$±$\sqrt[10]{3} -1$

We get two answers, but we look for a coherent value. So we take the positive one:

$i=11.6123174$≈12