Sinking funds

A sinking fund is a fund set up for a specific purpose at a future date. By making regular payments of size PS at regular intervals one accumulates a sum of money S at a certain date.

Payment size 

          S i
PS =              
     (1 + i)n - 1
where 
PS = payment size
S = sum you wish to accumulate
r = annual interest rate (a.p.r.)
m = number of payments per year also the number of compounding periods per year
t = time in years
     r
i =     = interest rate per compounding period
     m
n = m t = total number payments

Schedule

A sinking fund schedule consists of the following columns.
period :: payment size :: interest :: addition to sinking fund :: accumulated amount

Example:     A company sets up a sinking fund to be worth $30,000 in in 2 years. The
payments are made at the end of each quarter and earn 8% annual interest
compounded quarterly. Calculate the payment size and create a schedule. 
i = r/m = 0.08/4 = 0.02
n = 8
PS = S i/((1 + i)n - 1) = 30,000(0.02)/((1 + 0.02)8 - 1) = $3,495.29
Period Deposit Interest Addition
to fund 		Accumulated
amount
1 3495.29 0 3495.29 3495.29
2 3495.29 69.91 3565.20 7060.49
3 3495.29 141.21 3636.50 10697.00
4 3495.29 213.94 3709.23 14406.23
5 3495.29 288.12 3783.42 18189.65
6 3495.29 363.79 3859.09 22048.74
7 3495.29 440.97 3936.27 25985.01
8 3495.29 519.70 4014.99 30000.00

Exercise 


(1) Compute the size of the monthly payment needed to generate
    a sinking fund worth $500,000 in 10 years assuming an annual 
    interest of 8%.
     $2,733.05
     $48,518.27

Calculator

Amount to be accumulated
Annual interest rate as a decimal
Number of payments per year, also
Number of interest conversion periods per year
Number of years of payments



Payment size

If you do not mind waiting a few seconds press the following button to generate a schedule. The schedule shows how the payments and interest accumulate to the desired amount.

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