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# 12A. 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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