Christine contributes 100 each month to her 401(k). What...

Christine contributes $$\$ 100$$ each month to her 401(k). What will be the value of Christine's 401(k) after the 360 th deposit (30 years) if the per annum rate of return is assumed to be $12 \%$ compounded monthly?

Key Concepts

Annuities

An annuity refers to a series of equal payments made at regular intervals. In financial contexts, this concept is used to model regular contributions or withdrawals over time, where each payment accrues interest. The future value of an annuity is a common calculation that helps determine how much a series of payments will be worth at a future date.

Compound Interest

Compound interest is the process of earning interest on both the initial principal and the accumulated interest from previous periods. This concept accelerates the growth of an investment or debt over time and is central to understanding how factors such as interest rates and compounding frequency affect overall growth.

Periodic Compounding

Periodic compounding involves applying the interest rate to an investment at regular intervals, such as monthly, quarterly, or annually. The frequency of compounding plays a crucial role in the final value of an investment because the interest is calculated and added to the principal at each interval, leading to more rapid accumulation of interest over time.

Time Value of Money

The time value of money is a fundamental financial principle that stipulates money available at the present time is worth more than the identical sum in the future due to its potential earning capacity. This concept underpins many calculations in finance, such as determining the future value of annuities and the benefits of early and regular contributions.

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