Final answer:
To reach their retirement goal of $800,000 in 19 years without additional savings, the student's parents must earn approximately a 5.3% annual interest rate on their current savings of $350,000.
Step-by-step explanation:
The student is asking about compound interest and what annual interest rate their parents must earn to reach their retirement goal of $800,000 in 19 years without making any additional contributions beyond their current savings of $350,000.
To calculate the required annual interest rate, we can use the future value formula for compound interest:
FV = PV(1 + r)^n
Where:
- FV is the future value of the investment/loan, including interest,
- PV is the present value of the investment/loan (initial amount of money),
- r is the annual interest rate (decimal),
- n is the number of years the money is invested/borrowed for.
Given that FV = $800,000, PV = $350,000, and n = 19, we need to solve for r. Rearranging the formula to get r on one side gives us the following equation:
r = ((FV / PV)^(1/n)) - 1
Plugging in the numbers gives us:
r = (($800,000 / $350,000)^(1/19)) - 1
Calculating this we get:
r ≈ 0.053 or 5.3%
This means that the parents must earn an annual interest rate of approximately 5.3% to meet their retirement goal of $800,000 in 19 years, assuming no additional money is contributed.