What is the present value (PV) of 12,000 to be received in 5 years, assuming a discount rate of 8% compounded annually?
Answer (2)
The problem asks to calculate the present value of a future sum.
Apply the present value formula: P V = ( 1 + r ) n F V
Substitute the given values: P V = ( 1 + 0.08 ) 5 12000
Calculate the present value: P V ≈ 8167.00
Explanation
Understanding the Problem We need to calculate the present value (PV) of 12 , 000 t o b erece i v e d in 5 ye a rs w i t ha d i sco u n t r a t eo f 8 P V = ( 1 + r ) n F V $ where FV is the future value, r is the discount rate, and n is the number of years.
Identifying Given Values We are given: Future Value (FV) = $12,000 Time period (n) = 5 years Discount rate (r) = 8% = 0.08
Applying the Formula Substitute the given values into the present value formula: P V = ( 1 + 0.08 ) 5 12000
Calculating the Denominator Calculate the denominator: ( 1 + 0.08 ) 5 = ( 1.08 ) 5 ( 1.08 ) 5 ≈ 1.469328
Calculating the Present Value Now, calculate the present value: P V = 1.469328 12000 ≈ 8167.00
Final Answer Therefore, the present value is approximately $8167.00.
Examples
Understanding present value is crucial in financial planning. For instance, if you are promised $12,000 in 5 years and you know that a typical investment yields 8% annually, calculating the present value helps you determine how much that future payment is worth today. This concept is widely used in investment decisions, loan evaluations, and assessing the profitability of long-term projects. By discounting future cash flows, you can make informed decisions about whether an investment is worthwhile.
The present value of $12,000 to be received in 5 years at a discount rate of 8% compounded annually is approximately $8,167.00. This is calculated using the present value formula by discounting future cash flows. The formula accounts for the time value of money, which illustrates how today's value differs from a future value.
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