Compound Interest

maurizio13 SG

Ok.

If don't use calculator can use Newton-Raphson Method to approximate, after 20 iterations it's almost as accurate as my calculator.

Of course I used spreadsheet lah, only took few minutes, you can slowly use paper to calculate everything.

Master -_- SG

Arghhh Actuarial Mathematics and LT Stats...this module effectively has the record of leaving me sleepless for 6 nights

maurizio13 SG

Hmmm.......

Come to think of it, might be able to do linear interpolation or bisection method also.

maurizio13 SG

Linear Interpolation:

15%:

1,000 (1-(1+0.15)^20) / (1-(1+0.15)) = 102,443.58

20%:

1,000 (1-(1+0.20)^20) / (1-(1+0.20)) = 186,688.00

(i - 0.15) / (0.20 - 0.15) = (150,000.00 - 102,443.58) / (186,688.00 - 102,443.58)

i = 0.178225264

It's a rough approximation because the two interest rates are too far apart from the actual value (15% and 20%). If it's closer, the values would be more accurate.

maurizio13 SG

Linear Interpolation:

18%:

1,000 (1-(1+0.18)^20) / (1-(1+0.18)) = 146,627.97

18.3%:

1,000 (1-(1+0.183)^20) / (1-(1+0.183)) = 152,022.19

(i - 0.18) / (0.183 - 0.18) = (150,000 - 146,627.97) / (152,022.19 - 146,627.97)

i = 0.181875357

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