Find the amount of each payment to be made into a sinking...

Find the amount of each payment to be made into a sinking fund so that enough will be present to accumulate the following amounts. Payments are made at the end of each period.
$\$ 75,000$ money earns 6$\%$ compounded semiannually for 4$\frac{1}{2}$ years.

Key Concepts

Sinking Fund

A sinking fund is a savings fund established by making regular, fixed payments to accumulate a specific amount of money by a future date. Companies or individuals often set up sinking funds to repay debt, finance large expenditures, or replace capital assets, with contributions earning interest over time, helping the fund grow to the desired target amount.

Compound Interest

Compound interest refers to the process where interest earned on an initial principal amount is reinvested, so that in subsequent periods, interest is earned on both the original principal and the accumulated interest. This results in exponential growth of the fund, which is essential for accurately calculating the accumulation of funds over time.

Compounding Frequency

Compounding frequency determines how often interest is calculated and added to the principal within a given period. When interest is compounded semiannually, for example, the annual interest rate is divided into two equal parts and applied twice per year, thereby affecting the effective interest rate per period and the total number of compounding periods over the investment duration.

Annuity Payment Calculation

An annuity payment calculation is used to determine the fixed payment amount required at regular intervals to reach a desired future sum. The formula involves the future value, the interest rate per period, and the total number of payments. This approach is fundamental in planning regular investments, such as sinking funds, to ensure enough funds accumulate over time.

Time Value of Money

The time value of money is a core financial principle that recognizes the idea that a specific amount of money today has a greater value than the same amount in the future due to its potential earning capacity. This concept underpins many financial calculations, including those involving compound interest and annuities, and is essential when planning investments or savings strategies over time.

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