You want to retire in 25 years. You currently have $200.000 saved and you believe you need $1,200.000 at retirement. What annual interest rate will you need to earn to meet your goal?

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To determine the annual interest rate required to meet your retirement goal, we need to understand the concept of future value (FV). The future value is the worth of a current asset at a specified point in the future based on an estimated rate of growth. This is crucial for investors and financial planners as it helps them predict the future value of current investments.

## Explanation:

In annuity contracts, terms like present value (PV) and future value (FV) are frequently used. The future value of an annuity is the sum that will be accumulated over time, whereas the present value is the amount that must be invested now to achieve a desired future payment.

Number of years until retirement (n):25 yearsCurrent savings balance (P):$200,000Future value of balance required at retirement (FV):$1,200,000The future value formula is:

FV = P × (1 + r)

^{n}Where:

Plugging in the values:

1,200,000 = 200,000 × (1 + r)

^{25}To isolate r:

1,200,000 / 200,000 = (1 + r)

^{25}6 = (1 + r)

^{25}Taking the 25th root of both sides to solve for r:

1 + r = 6

^{1/25}1 + r ≈ 1.074301177

r ≈ 0.074301177

Converting to a percentage:

r ≈ 7.43%

## Final Answer:

Thus, the required annual interest rate to meet your retirement goal is

7.43%.