Find the periodic payments necessary to accumulate the given...

Find the periodic payments necessary to accumulate the given amount in an annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits.) [HINT: See Quick Example 2.] $\$ 100,000$ in a fund paying $7 \%$ per year, with quarterly payments for 20 years

Find the periodic payments necessary to accumulate the given amount in an annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits.) [HINT: See Quick Example 2.]
$\$ 100,000$ in a fund paying $7 \%$ per year, with quarterly payments for 20 years

Key Concepts

Future Value of an Ordinary Annuity

This concept involves accumulating a series of equal periodic payments that are made at the end of each period, with each deposit earning interest over time. The future value of an annuity calculates the total amount that these periodic deposits will reach by the end of the investment period, based on a given interest rate and number of periods.

Periodic Interest Rate Conversion

When dealing with interest that is compounded more frequently than once per year, the annual interest rate must be converted into a periodic rate that corresponds to the compounding interval. This is done by dividing the annual rate by the number of compounding periods per year, thereby aligning the rate with the frequency of deposits.

Compounding Frequency and Number of Periods

Compounding frequency refers to how often interest is applied to the account balance, such as quarterly in this case. The total number of compounding periods is determined by multiplying the number of years by the number of compounding periods per year. This total is essential in the annuity formula as it affects the accumulation of interest over time.

Annuity Payment Calculation

Using the future value of an annuity formula, the periodic payment necessary to reach a desired accumulated amount can be computed. The formula rearranges the accumulated value equation to solve for the periodic payment by linking the known future value, periodic interest rate, and number of periods.

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