# Simple Interest calculation on rent of specific period till date of payment

Hi I have to calculate simple interest on Rent of Rs.10,000 @6%. There are two parts to my problem.

1. Calculation of simple interest on rent amounts due for 41 months progressively i.e. as rents keep becoming due, till date of payment i.e. total 140 months.

2. Then calculation of simple interest on entire rent amount of 41 months for 99 further months i.e. till date of payment

For Simple Interest it may be useful to first find the monthly interest for a single rent payment (Rs. 10,000). Assuming a annual nominal rate of 6% (confirm that it is in fact annual) the interests for a single month of rent would be 10,000*6%/12 = Rs. 50.

I am assuming rent payments are due at the beginning of the rent period, therefore after 1 month you have 50 of accrued interest. By progressively I take it that your first month of rent would have generated 41*50 = Rs. 2,050 in interests, your second month 40*50 = Rs. 2,000, and so on, to add up all results. Alternatively, you can use the formula to sum a series of numbers `S= n(n+1)/2` (1 to 41) and multiply by 50. With n=41 you'll get Rs. 43,050.

If I understood the question correctly, the months due up until now will continue to accrue interests for a further 99 months. 41*10,000*6%/12 = Rs. 2,050 monthly. Totaling Rs. 202,950 for the remaining 99 months.

Additionally however, during the following 99 months (until 140) each month will accrue interests as well. The first month will accrue 99 months of interests 99*50 = Rs. 4,950, the next month 98*50 = Rs. 4,900, and so on. Using n=99 in the series formula, you'll end up with Rs. 247,500.

All accrued interests (not compounding) should be Rs. 493,500. Which can also be found solving:

`S= n(n+1)/2 with n=140`, and multiplying the result by 50.

`(140*(140+1)/2)*50 = 493,500`