Question

Your parents will retire in 15 years. They currently have $330,000 saved, and they think they will need $1,500,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.

Answer 1

To reach their retirement goal, your parents must earn an annual interest rate of approximately 15.56%.

Step-by-step explanation:

To determine the annual interest rate your parents must earn to reach their retirement goal, we can use the compound interest formula. The formula is
`A = P(1 + r)^n`, where A is the future value, P is the present value, r is the annual interest rate, and n is the number of years. In this case, we have P = $330,000, A = $1,500,000, and n = 15. We need to solve for r.

Plugging in the values, we get $1,500,000 =
`$330,000(1 + r)^(15)`. To solve for r, we need to isolate it. Divide both sides by $330,000:
`(1 + r)^(15)` = 4.54545455. Next, take the 15th root of both sides: 1 + r = 1.15562735. Finally, subtract 1 from both sides to isolate r: r = 0.1556.

Your parents must earn an annual interest rate of approximately 15.56% to reach their retirement goal.