Artificial intelligent assistant

Calculating diminishing interest amount The agent says he will loan an amount of 24,660 dollars and let me pay 414 dollars monthly + interest of 1% **per Month** on the diminishing balance. How do I calculate the time by which I should be paid up? What is the total interest I pay in this scenario ?

The easy way to do this is with an excel spreadsheet.

Put 24,660 in the first row. and put 24,660*(1.01) - 414 in the row below, and spread it down until the number goes negative.

The other way to do it is to derive a formula.

The NPV of future cashflows is:

$414 \sum_\limits{i=1}^n (1.01)^{-i} = 24,660\\\ 414 \frac {1-(1.01)^{-n}}{0.01} = 24,660\\\ n = -\frac {\log(1-\frac {24,660}{414}0.01)}{\log 1.01}$

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