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Finance

`d0=: %@>:@(] % 100"_) #. \|.@[`	Present value flows x at y%
`d1=: >:@(] % 100"_) #. [`	Future value of flows x at interest rate y
`d2=: ([: >: [ % 100"_) ^/ ]`	Amount of 1 at x% for y periods
`d3=: 13 : '\|: y.%-.(>:y.) ^/ -x.'`	Annuity coefficient: periods x at rate y
`d4=: [ d3 [: m5 ]`	Annuity coefficient: periods x at y %
`m5=: 0.01&*`	Rate from percent
`m6=: 100&*`	Percent from rate
`d7=: <: @ ((^%)~ >:)`	Modal rate from annual rate
`d8=: stretch=: [ $ ] , ($ ,: @ {:)`	Stretch y to length x
`d9=: */\ @ (1&,) @ (stretch >:)`	Accumulate at y for period x
`m10=: (% {.) @ (\|.@(+/\)@i.@>:)`	Outstanding balances on rule of 78
`m11=: }.%}:`	Rate of change from amounts
`m12=: 2&((%~)/\)`	Rate of change from amounts
`d13=:4 :'r+/\y.%r=:/\1,x.$~<:#y.'`	Accumulate deposits y at x
`d14=: [+2: -/\ [: >./\ 0:,[: +/\ -`	Work done; x=capacity, y=demand

Convert an annual interest rate of 7% to a monthly rate.

   ]m=: 12 d7 0.07
0.00565415
   (1 + m)^12
1.07

Calculate the amount of 1 for 5 periods at rates of 7% for the first two years and 6% thereafter. The function d9 uses d8 to fill out the term with the last given rate.

   5 d9 0.07 0.07 0.06
1 1.07 1.1449 1.21359 1.28641 1.36359

Calculate the declining balances for a year for 1 using the rule of 78.

   ,.m10 12
        1
 0.846154
 0.705128
 0.576923
 0.461538
 0.358974
 0.269231
 0.192308
 0.128205
0.0769231
0.0384615
0.0128205
        0
   x: m10 12
1 11r13 55r78 15r26 6r13 14r39 7r26 5r26 5r39 1r13 1r26 1r78 0
   78 * m10 12
78 66 55 45 36 28 21 15 10 6 3 1 0

Calculate the balances after periodic payments of 100, 100, 200, and 200 are made at rates of 10%, 10%, and 5%.

   1.10 1.10 1.05 m13 100 100 200 200
100 210 431 652.55

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