Answer:
The (minimum) annual interest rate should be at 7.28%
Explanation:
Compound Interest
An investment consisting of a principal P, (or present value) earns interest on each period considering the previous period's amount including the interest earned (no withdrawals). This situation is defined as an investment in compound interest unlike simple interest, where each interest amount is withdrawn and the new principal is P again.
To find the future value (FV) of an investment with an interest annual rate i during n years is
[tex]\displaystyle FV=P(1+i)^n[/tex]
If needed, we can solve the equation for i. Dividing by P:
[tex]\displaystyle \frac{FV}{P}=(1+i)^n[/tex]
Taking the nth-root:
[tex]\displaystyle \sqrt[n]{\frac{FV}{P}} =1+i[/tex]
Finally:
[tex]\displaystyle i=\sqrt[n]{\frac{FV}{P}} -1[/tex]
The parents will retire in n=27 years and they currently have P=$360,000 as an initial investment that they want to become into their retirement funds. Let's calculate the needed interest rate:
[tex]\displaystyle i=\sqrt[27]{\frac{2,400,000}{360,000}} -1[/tex]
[tex]\displaystyle i=1.0728-1=0.0728[/tex]
[tex]i=7.28\%[/tex]
The (minimum) annual interest rate should be at 7.28%
