What is the present value (PV) of 24,000 to be received in 6 years, assuming a discount rate of 10% compounded annually?
Answer (2)
Define the present value (PV) formula: P V = ( 1 + r ) t F V .
Substitute the given values: F V = 24000 , r = 0.10 , and t = 6 .
Calculate the present value: P V = ( 1 + 0.10 ) 6 24000 = 1.771561 24000 ≈ 13547.37 .
The present value of 24,000 to be received in 6 years, assuming a discount rate of 10% compounded annually is 13547.37 .
Explanation
Understanding the Problem We are asked to find the present value (PV) of a future sum of money. We are given the future value (FV), the time period (t), and the discount rate (r).
Present Value Formula The formula for present value is: P V = ( 1 + r ) t F V where:
PV is the present value
FV is the future value
r is the discount rate (as a decimal)
t is the number of years
Given Values We are given:
FV = 24,000
r = 10% = 0.10
t = 6 years
Calculating Present Value Substitute the given values into the formula: P V = ( 1 + 0.10 ) 6 24000 P V = ( 1.10 ) 6 24000 P V = 1.771561 24000 P V = 13547.37
Final Answer The present value is approximately 13,547.37.
Examples
Understanding present value is crucial in financial planning. For instance, if you want to have $24,000 in 6 years for your child's college fund and you can earn 10% annually on your investments, calculating the present value tells you how much you need to invest today. This concept is also used in evaluating investment opportunities, where you compare the present value of future cash flows to the initial investment to determine if the investment is worthwhile. By discounting future values to their present value, you can make informed financial decisions.
The present value of $24,000 to be received in 6 years at a 10% annual discount rate is approximately $13,547.37. This is calculated using the present value formula, which accounts for the time value of money. Knowing the present value helps individuals make better financial decisions regarding investments.
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