Question

If someone opens a savings account with a 1% intrest rate per day and they put $30 in a month how much will they have in 12 months

Answer 1

wow thats a great rate
anyway, assuming a uniform 30-day month
each month the effective interest is the daily rate compounded 30 times
--> 1.01^30 = 1.3478
so each month, 30 is deposited and the balance earns 34.78% interest
the sum after 12 months looks like a geometric progression
\[S = 30(1.3478) + 30(1.3478)^{2} +...30(1.3478)^{12}\]
factor out the 30, then use formula for finding sum of geometric progression
sum = a(r^n -1)/(r-1)
\[S = 30[\frac{1.3478(1.3478^{12} -1)}{1.3478 -1}]\]
the result is the balance after 12 months...pretty good return for only depositing 360 :)
Note: it is approximate due to rounding...to be more exact use (1.01^30) instead of 1.3478