



 
Kelly, The amount, A(t), that $P becomes after t years at an interest rate of r% compounded m times per year is
In your example A(1) = 100000(1+.005/365)^{365} = $100501.25. This is a ridiculously low rate of interest and I suspect that who ever is offering you this is counting on you not being able to do the calculations. Beware! Penny
Kelly wrote back
Kelly, The annual interest rate is 0.5%, which as a decimal is 0.005, so the daily interest rate is
plus the interest
In other words, at the end of the first day you receive
This is the amount you invest on the second day so at the end of the second day you have what you invested
plus the interest
which is
This is the amount you invest on the third day so at the end of the third day you have
The pattern continues and hence at the end of one year you have
Penny
Hi Kelly, Perhaps you have been offered a very strange investment indeed. Normally, interest rates are quoted as annual interest rates. Penny has interpreted your situation that way and I believe this is almost certainly the case for your situation. There is however a slight chance that you really have been offered the rate of 0.5% accrued daily (rather than 1/365 of that). If so, (and this is a big "if" that would have to be very clearly spelled out in the contract  or better yet, converted to the equivalent normal annual form), then your total at the end of one year would be:
but here r is the rate per DAY, m is the number of times paid DAILY (1), and t is the number of DAYS, so
The equivalent annual (normal) rate of interest compounded daily is
which works out to
This is too good to be true  I'd certainly consult a lawyer and perhaps the police before I'd invest my money here. Stephen La Rocque.>  


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