You have 42,180.53 in a brokerage account, and you plan to...

You have $\$ 42,180.53$ in a brokerage account, and you plan to deposit an additional $\$ 5,000$ at the end of every future year until your account totals $\$ 250,000 .$ You expect to earn $12 \%$ annually on the account. How many years will it take to reach your goal?

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Key Concepts

Compound Interest

Compound interest refers to the process whereby investment earnings, from either capital gains or interest, earn additional returns over time. It involves calculating interest on both the initial principal and the accumulated interest from previous periods, leading to exponential growth in the value of an investment.

Annuity

An annuity is a series of regular, equal payments made at consistent time intervals. In financial calculations, annuities are used to determine the future value of a series of deposits or the present value of a series of future payments, accounting for the effects of compound interest over time.

Future Value Calculation

Future value calculations determine the amount of money an investment will grow to over a period at a given interest rate, considering both an initial amount and any additional contributions, such as regular deposits. This involves summing the compounded future values of the initial lump sum and the periodic payments.

Logarithmic Equation Solving

Logarithmic equation solving is used when the variable to be determined is an exponent in an exponential growth equation. In financial contexts, this technique allows one to solve for the number of periods required to achieve a specific future value, given the interest rate and the amounts involved.

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