Time Value of Money - Present Value vs Future Value Analysis

Time Value of Money

Concept of Present Value (PV)

• Present Value refers to the current worth of a sum of money that is to be received in the future, discounted at a specific interest rate.

Given Problem

• Question: Which amount is worth more at 12%, compounded annually: $4,000 in hand today or $3,500 due in 6 years?

Given Data

1. Amount Today: $4,000
2. Amount in Future: $3,500
3. Interest Rate: 12% per annum
4. Time: 6 years

Calculation of Future Value (FV)

• To evaluate the amount due in the future in present value terms, we utilize the formula for future value: FV = PV imes (1 + r)^n Where:
  • FV = future value
  • PV = present value
  • r = annual interest rate (expressed as a decimal)
  • n = number of years

Calculation of Present Value of $3,500

1. Convert the interest rate from percentage to decimal:

   • r = rac{12}{100} = 0.12

2. Calculate Present Value (PV) of $3,500

   • Rearranging the FV formula:
     PV = rac{FV}{(1 + r)^n}
   • Plug in the values:
     PV = rac{3500}{(1 + 0.12)^6}
   • Calculate:
     PV = rac{3500}{(1.12)^6}
   • Now calculate $(1.12)^6$
   • Approximately: (1.12)^6
     ightarrow 1.9738
   • Thus:
     PV
     ightarrow rac{3500}{1.9738}
     ightarrow 1775.77 (approximately)

Comparison of PV and Cash Amount Today

• Amount in Hand Today: $4,000
• Present Value of Future Amount ($3,500 in 6 years): $1775.77 (approximately)

Conclusion

• Comparing the two:
  • $4,000 (today) is greater than $1,775.77 (the present value of $3,500 due in 6 years).
• Therefore, $4,000 in hand today is worth more than $3,500 due in 6 years at an interest rate of 12%, compounded annually.