How to use it
- Choose Value of payments to value a series, or Payment for a lump sum to find the payment.
- Enter the payment (or the lump sum), the yearly interest rate and the number of years.
- Pick how often payments are made and whether they fall at the end or the start of each period.
How it works
With i as the rate per period (yearly rate ÷ payments per year) and n as the number of payments:
- Present value = payment × (1 − (1 + i)^−n) ÷ i
- Future value = payment × ((1 + i)^n − 1) ÷ i
- With a 0% rate both are simply payment × n.
- Payments at the start of each period multiply both by (1 + i).
Worked example
Receiving 1,000 at the end of each year for 10 years at 5% is worth 7,721.73 today and 12,577.89 at the end of year 10. You receive 10,000 in total, so 2,577.89 of the future value is interest. If the payments come at the start of each year, the values rise to 8,107.82 and 13,206.79.
To match a lump sum of 10,000 with monthly payments over one year at 12%, you need 888.49 a month.
Tips
- Small changes in the rate matter more the longer the term is, so try a few rates.
- Rates are nominal yearly rates split evenly across periods.
- These are estimates, not financial advice.