CalculateY
Quick Answer
A $100,000 lump sum due in 10 years at a 5% discount rate has an estimated present value of approximately $61,391, meaning that amount invested today at 5% would grow to $100,000 in 10 years.
Common Examples
| Input | Result |
|---|---|
| $50,000 lump sum in 5 years at 4% discount rate | Estimated present value: approximately $41,096 |
| $100,000 lump sum in 10 years at 5% discount rate | Estimated present value: approximately $61,391 |
| $250,000 lump sum in 20 years at 6% discount rate | Estimated present value: approximately $77,950 |
| $10,000/year annuity for 15 years at 5% discount rate | Estimated present value: approximately $103,797 |
| $5,000/year annuity for 30 years at 4% discount rate | Estimated present value: approximately $86,461 |
How It Works
This calculator uses the time value of money principle: a dollar today is worth more than a dollar in the future because it can be invested and earn a return. The discount rate represents the expected rate of return or opportunity cost.
Lump Sum Present Value:
PV = FV / (1 + r)^n
Where:
- PV = estimated present value
- FV = future value (the amount to be received)
- r = annual discount rate (as a decimal)
- n = number of years until payment
This answers the question: “How much would I need to invest today at rate r to have FV in n years?”
Annuity Present Value:
PV = PMT x [(1 - (1 + r)^(-n)) / r]
Where:
- PMT = annual payment amount
- r = annual discount rate
- n = number of payment periods (years)
This calculates the lump sum equivalent of receiving a series of equal annual payments. It answers: “What is the total value today of receiving PMT per year for n years?”
Discount Amount:
The discount is the difference between the total future cash flows and their present value. It represents the time value of money, or the amount that would be earned through interest if the present value were invested at the discount rate.
Worked Example
For a $100,000 lump sum due in 10 years at a 5% discount rate: PV = $100,000 / (1 + 0.05)^10 = $100,000 / (1.05)^10 = $100,000 / 1.6289 = approximately $61,391. The discount is $100,000 - $61,391 = approximately $38,609. This means investing approximately $61,391 today at 5% annual return would grow to $100,000 in 10 years.
For a $10,000/year annuity over 15 years at 5%: PV = $10,000 x [(1 - (1.05)^(-15)) / 0.05] = $10,000 x [(1 - 0.4810) / 0.05] = $10,000 x [0.5190 / 0.05] = $10,000 x 10.3797 = approximately $103,797. The total undiscounted payments equal $150,000 ($10,000 x 15), so the discount is approximately $46,203.
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