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

a) About 12%

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