A department has ordered 8 new Dell computers at a cost of ...

A department has ordered 8 new Dell computers at a cost of $\$ 2309$ each. The order will not be delivered for 6 months. What amount could the department deposit in a special 6 -month CD paying 4.79$\%$ compounded monthly to have enough to pay for the machines at time of delivery?

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Key Concepts

Compound Interest

Compound interest involves earning interest on both the principal and the accumulated interest from previous periods. It is calculated using the formula FV = PV × (1 + r/n)^(n×t), where r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years. This concept is used to determine how an initial deposit grows over time with periodic interest additions.

Present Value

Present value is the current amount of money that must be invested to reach a desired future sum when earning interest at a given rate over a specific period. It reflects the time value of money by discounting a future amount back to the present using the compound interest formula, effectively answering the question of how much money today will grow to a needed amount in the future.

Compounding Frequency

Compounding frequency refers to the number of times interest is calculated and added to the account balance within a year. For example, monthly compounding applies interest 12 times a year, which results in interest being calculated on an increasingly higher balance, leading to a greater accumulation of interest over time compared to less frequent compounding intervals.

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