What is the present value (PV) of 22,000 to be received in 6 years, assuming a discount rate of 10% compounded annually?
Answer (2)
Define the present value formula: P V = ( 1 + r ) t F V .
Substitute the given values: F V = 22000 , r = 0.10 , and t = 6 .
Calculate ( 1.10 ) 6 = 1.771561 .
Calculate the present value: P V = 1.771561 22000 ≈ 12 , 418.43 .
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 = 22,000
r = 10% = 0.10
t = 6 years
Calculations Substitute the given values into the formula: P V = ( 1 + 0.10 ) 6 22000 P V = ( 1.10 ) 6 22000 First, calculate ( 1.10 ) 6 :
( 1.10 ) 6 = 1.771561
Final Calculation Now, calculate the present value: P V = 1.771561 22000 = 12418.426461183099 Rounding to two decimal places, we get PV = 12,418.43
Conclusion The present value of 22,000 to be received in 6 years, assuming a discount rate of 10% compounded annually, is approximately ₹12,418.43.
Examples
Understanding present value is crucial in financial planning. For instance, if you're promised a bonus of $22,000 in 6 years and you want to know how much that's worth today, assuming a 10% annual discount rate, calculating the present value helps. It tells you that the future $22,000 is equivalent to having $12,418.43 today, considering the time value of money and potential investment returns. This concept is vital for making informed decisions about investments, savings, and loans.
The present value of $22,000 to be received in 6 years, given a 10% discount rate compounded annually, is approximately $12,418.43. This calculation reflects how future money is worth less today due to the time value of money. Understanding this concept is important for financial decision-making regarding savings and investments.
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