# What formula has bank used in this situation?

This is the bank fixed deposit's start date and end date with the principal and maturity amounts. The rate is 7% p.a.

Could anyone help with how the bank has calculated this maturity amount?

• @keshlam This is the indian numbering system (ending with one group of 3 digits, the rest groups of 2). Monthly compounding seems to fit. Commented Feb 10, 2023 at 11:36
• That is 599 days and I calculate you should get 1.1174 times your original amount, but you actually get 1.1208 times, which is about the amount you would get for 615 days at 7.000%, or 599 days at 7.182% interest Commented Feb 10, 2023 at 14:23
• Is this daily compounding, or monthly? The latter is much, much more common. Commented Feb 10, 2023 at 14:45
• It’s quarterly compounding. Commented Feb 11, 2023 at 13:01

You get pretty close if you use 30-day months and monthly compounding. In your case, the monthly rate would be 7%/12 or 0.5833%, and there are 19 full months between those dates. So the balance after 19 full months would be:

``````42,01,593 * (1+0.0058333)^(19)  = 46,92,543
``````

For the remaining 21 days (from 17-6-2024 to 8-7-2024), the daily interest rate would be

``````46,92,543 * 0.0058333 / 30 = 912.44
``````

So the remaining interest for those 21 days would be

``````912.44 * 21 = 19,161
``````

And the total final balance would be

``````46,92,544 + 19,161 = 47,11,706
``````

There are probably some differences in when each compounding period starts (e.g. the periods may start on the first of each month and you get a partial month's interest at the beginning) or differences in daycount, but that's the general idea - compound the balance using some periodic rate and then add in the daily remainder.

Your bank statement or initiation documents probably outline the exact day count convention and interest calculation method.

• I think you're missing the exponential-growth aspect of compounding... Commented Feb 10, 2023 at 17:22
• @keshlam No, the first formula represents monthly compounding. Bank accounts do not typically compound daily so the remaining interest is not exponentially compounded. Commented Feb 10, 2023 at 17:35
• What I'm disagreeing on is whether the monthly rate is 7%/12 or (1.07^(-12))-1. I'll note that by applying the latter my result came out closer than yours without considering the factional month. But yes, if you want the exact formula being used you can always ask the bank; this is probably in the account documents. Commented Feb 10, 2023 at 17:42
• can I ask Why cacualate 21 days ? {912.44 * 21 = 19,161} Commented Feb 11, 2023 at 6:42
• There are 21 days between the last day of the last full month (17-06-2024) and the given end date (08-07-2024) Commented Feb 12, 2023 at 20:16

Assuming monthly compounding (which is what most banks use, at least in the US), this should be twelvth root of 1.07 to get the monthly interest multiplier, raised to the power of -- is that 19 compounding dates? -- to get the multiplier over the entire time period, multiplied by the starting amount to produce the final amount. Standard compound interest formulas.

Working that through:

• (1.07^-12) = 1.005654 (monthly multiplier)
• ^19 = 1.11307 (multiplier over 19 months)
• x 42,01,593 = 46,76,687 (rounding up)

Not exactly the same number, but close.

If they're doing daily compounding the math is similar but the result would be a bit higher. Trying it that way, I get:

• (1.07 ^ -365) = 1.0001853833415704 (daily interest multiplier, assuming 365 days per year)
• ^ 599 = 1.1174332676365512 (over 599 days)
• x 42,01,593 = 46,94,999.

Closer but still not exact; I suspect that the remaining disagreement really is round-off differences between their computation and mine. Since the difference is in your favor, I wouldn't suggest complaining. :-)

For a more exact answer, ask the bank when they're compounding and how many digits they're keeping in the calculations.

• You say it's quarterly compounding... OK, I've demonstrated how to do it, fourth root of the apr, to the power of however many quarters' compounding you got. If that comes out low, play with rounding and/or see if adding another quarter makes it agree; they may not be compounding on exactly the day you expect. Or ask them. Seriously, they must have a standard document which answers this. Commented Feb 12, 2023 at 2:41