You have currently accumulated $50,000 thus far for your retirement, and are planning to have $1,000,000 in 30 years when you retire.If you can add $6,000 each year to your retirement fund, what interest rate do you need to have in order to achieve your retirement goal?
A)6.17%
B)7.24%
C)9.04%
D)10.71%

Question

Quizplus · Accepted Answer

To solve this, we use the future value of a series formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) + P_0 \times (1 + r)^n$, where $FV$ is the future value of the fund, $P$ is the annual addition, $r$ is the annual interest rate, $n$ is the number of years, and $P_0$ is the initial amount. We are solving for $r$ given $FV = \$1,000,000$, $P = \$6,000$, $n = 30$, and $P_0 = \$50,000$. Plugging these values into a financial calculator or using an iterative method to solve for $r$, we find that the interest rate needed is approximately 7.24%.

You Have Currently Accumulated $50,000 Thus Far for Your Retirement