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A college student plans to deposit $340 in a savings account at the end of each quarter for the next 22 years. Interest is earned at a rate of 6% per year and is compounded quarterly. What is the future value of this annuity?

User Spinlok
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Final answer:

To determine the future value of an annuity where $340 is deposited quarterly for 22 years at a 6% annual interest rate, compounded quarterly, we use the formula for compound interest. The annual rate is converted to a quarterly rate, and the number of years is converted to the number of quarters, before applying the formula.

Step-by-step explanation:

The future value of an annuity can be calculated using the formula for the future value of an annuity due to compound interest. In this case, a college student plans to deposit $340 at the end of each quarter for 22 years, with an interest rate of 6% per year, compounded quarterly.

The formula we'll use is FV = P × {[(1 + r)n - 1] / r}, where FV is the future value, P is the periodic payment, r is the interest rate per period, and n is the total number of payments.

To solve this, we'll convert the annual interest rate to a quarterly one by dividing it by 4, giving us 1.5% or 0.015 per quarter.

We'll also convert the years into quarters, multiplying 22 years by 4, to get a total of 88 payments. Plugging these values into the formula, we calculate the future value of the annuity.

User Merkost
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