# n = number of payments
# d = discount 
# r = monthly inflation rate
present_value(n, d, r) = sum((1-d)/n * (1/(1+r))^(i-1), i, 1, n)
r0 = root(present_value(12,0,r) - present_value(3,0.3,r), r, 0, 0.2)

PRINTF "the tipping monthly inflation is %g (that means %.1f%% per month and %.1f%% per year)" r0 100*r0 100*(1+r0)^12

PRINT

PRINTF "with 12 payments no discount with r = %g you pay %.3f"  r0+0.01 present_value(12,0,r0+0.01)
PRINTF "with  3 payments and 30%% off with r = %g you pay %.3f" r0+0.01 present_value(3,0.3,r0+0.01)

PRINT

PRINTF "with 12 payments no discount with r = %g you pay %.3f"  r0-0.01 present_value(12,0,r0-0.01)
PRINTF "with  3 payments and 30%% off with r = %g you pay %.3f" r0-0.01 present_value(3,0.3,r0-0.01)