Business Mathematics
Periodic payments
Haaga-Helia / KeiKa
Page 1
Periodic payments
FV = Future Value of all periodic payments
PV = Present Value of all periodic payments
pmt = Payment (= constant amount of money paid regularly). Also called an Annuity
p%
i = interest rate for the payment period in a decimal format [ i =
]
100
n = number of payments
1. Future value
FV 
2. Present value
(1  i ) n  1
 pmt
i
PV 
3. Payment (from the future value)
pmt 
i
 FV
(1  i ) n  1
(1  i ) n  1
 pmt
(1  i ) n  i
4. Payment (from the present value)
pmt 
(1  i ) n  i
 PV
(1  i) n  1
Example 1.
250 € is paid monthly for 10 years. The annual net interest rate is 2,1%.
pmt = 250 €
0,021
i=
= 0,00175
12
n = 10 × 12 = 120
1,00175120  1
FV 
 250 €  33 350 €
0,00175
Example 2.
The loan can be paid back with 400 € monthly payments. Loan time is 5 years and the
interest is 4,2%. How big the loan can be? (Note! Loan = Present value)
pmt = 400 €
0,042
i=
= 0,0035
12
n = 5 × 12 = 60
1,003560  1
 400 €  21 613 €
Loan = PV 
1,003560  0,0035
Business Mathematics
Periodic payments
Haaga-Helia / KeiKa
Page 2
Example 3.
How much must a person save monthly if he wants to have 25 000 € after 7 years?
The annual interest rate is 1,8% and source tax is 28%.
FV = 25 000 €
0,018
 0,72 = 0,00108
i=
12
(note: source tax is removed by multiplying with 0,72)
pmt 
n = 7 × 12 = 84
0,00108
 25 000 €  284,48 €
1,0010884  1
Example 4.
What is the equal monthly payment for a 120 000 € loan, if the loan time is 20 years
and the interest is 4,44% ?
PV = 120 000 €
0,0444
i=
= 0,0037
12
n = 20 × 12 = 240
pmt 
1,0037 240  0,0037
 120 000 €  755,30 €
1,0037 240  1