Time Value of Money Calculator
Calculate PVIF, FVIF, PVIFA and FVIFA; analyse present value, future value, annuities, loan installments and savings plans in one tool.
Calculate present and future cash flows, annuities and loan installments.
Results
Notes on the time value of money
What is the time value of money?
A lira received today can be invested and is therefore worth more than a lira received later. Present and future values convert cash flows across time with an interest (discount) rate.
What is PVIF?
PVIF(i,n) = (1+i)^(-n) is the discount factor for a single future cash flow. Multiply the future amount by PVIF to obtain its present value.
What is FVIF?
FVIF(i,n) = (1+i)^n compounds a single present amount forward n periods. Multiply PV by FVIF to obtain FV.
What is PVIFA?
PVIFA(i,n) = [1 − (1+i)^(-n)] / i is the ordinary-annuity present-value factor. PVA = PMT × PVIFA. If i = 0, PVIFA = n.
What is FVIFA?
FVIFA(i,n) = [(1+i)^n − 1] / i is the ordinary-annuity future-value factor. FVA = PMT × FVIFA. If i = 0, FVIFA = n.
What is the difference between ordinary and due annuities?
An ordinary annuity pays at the end of each period (typical loan installment). An annuity due pays at the beginning. Due factors equal ordinary factors multiplied by (1+i).
How is a loan installment calculated?
The constant end-of-period installment is PMT = PV / PVIFA. Equivalently, PMT = PV × i / [1 − (1+i)^(-n)]. A balloon is subtracted at present value before dividing by PVIFA.
What is the difference between nominal and effective rates?
A nominal annual rate divided by the number of periods gives the periodic rate (i = r/p). An effective annual rate already includes intra-year compounding: i = (1+EAR)^(1/p) − 1.
Note: This calculator is intended for financial education and decision support. Results depend on the assumptions you enter; taxes, fees, commissions and other contractual costs charged by banks or counterparties must be considered separately.