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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 ?

Maximus
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  • You might be able to find a mortgage calculator on line and fool it into giving you an (approximate) answer to this question. Or set it up in a spreadsheet. Maybe someone will provide an answer here. – Ethan Bolker Jan 25 '18 at 20:59
  • So the first interest amount would be $1%$ of $24660-414=24246$, or $242.46$? – John Jan 25 '18 at 21:01
  • Have you tried any calculations yourself? Do you know geometric series? – David Quinn Jan 25 '18 at 21:01

3 Answers3

1

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:

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

Doug M
  • 57,877
  • Isn't it $(24,660 - 414)*1.01$? The question says "1% per Month on the diminishing balance" – Weather Vane Jan 25 '18 at 21:32
  • It depends, did you make your payment on the first day of the month, or the last day of the month? The "traditional" way to calculate it is to first accrue your interest, and then a payment. If you do it the other way around you will always be one payment ahead. i.e. you made your first payment on the day you borrowed the money. But, if you adjust your initial loan balance for the first month's AI, you end up in the same place. – Doug M Jan 25 '18 at 22:22
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By C program,

#include<stdio.h>

int main()
{
    double capital = 24660;
    double interest = 0;
    double juice;
    int months = 0;
    while (capital > 0) {
        capital -= 414;
        juice = capital / 100;
        capital += juice;
        interest += juice;
        months++;
    }
    printf("Balance  %.2f\n", capital);
    printf("Interest %.2f\n", interest);
    printf("Months   %d\n",   months);
}

It will take you 90 months but you will have overpaid by $190 in the last month, and added about half the loan in interest.

Balance  -189.84
Interest 12410.16
Months   90
Weather Vane
  • 385
1

Assuming that interest accrues immediately after the loan is made, and that the first payment is made after one month, then after one month you owe $$24660\times1.01-414$$

Similarly, after 2 months you owe $$(24660\times 1.01-414)\times1.01-414$$ $$=24660\times1.01^2-414(1+1.01)$$

After $n$ months you owe nothing, so you will have $$24660\times1.01^n-414(1+1.01+1.01^2+...)=0$$

So, using the formula for the sum of a geometric series, , we have to solve for $n$ the equation $$24660\times1.01^n=414\times\frac{1.01^n-1}{1.01-1}$$

This rearranges to give $$1.01^n=\frac{41400}{41400-24660}\implies n=90.99997...$$

So it looks like you make 90 payments of 414 and your last payment is 409.89 plus interest for one month, so 413.99.

David Quinn
  • 34,121