   SEARCH HOME Math Central Quandaries & Queries  Subject: interest compounded daily Name: Kelly Who are you: Other Dear Sir's , I have made an investment that offers one-half of 1% interest compounded daily. What would that interest calculate to with a $100,000.00 investment for one year ? I have not found a calculative formula that will calculate these figures ... Please HELP !!! Thank-you. Kelly Kelly, The amount, A(t), that$P becomes after t years at an interest rate of r% compounded m times per year is

A(t) = P(1+r/m)mt.

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 Dear Penny , Please explain the answer that You gave me regarding the amount of interest that I'll earn on$100K investment @.005% interest compounded daily... Please ... I thought that the interest compounded daily , could be more than $500.00 ? Am I "WRONG" ??? Please reply. Thankx. Kelly Kelly, The annual interest rate is 0.5%, which as a decimal is 0.005, so the daily interest rate is 0.005/365. Thus if you invest$100,000 at this rate for one day you receive, at the end of the day, what you invested

$1000,000 plus the interest 0.005/365 $100,000

In other words, at the end of the first day you receive

$100,000 + 0.005/365 $100,000 = $100,000 (1 + 0.005/365) This is the amount you invest on the second day so at the end of the second day you have what you invested$100,000 (1 + 0.005/365)

plus the interest

0.005/365 $100,000 (1 + 0.005/365) which is$100,000 (1 + 0.005/365) + 0.005/365 $100,000 (1 + 0.005/365) =$100,000 (1 + 0.005/365) (1 + 0.005/365)

= $100,000 (1 + 0.005/365)2 This is the amount you invest on the third day so at the end of the third day you have$100,000 (1 + 0.005/365)3

The pattern continues and hence at the end of one year you have

$100,000 (1 + 0.005/365)365 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: A(t) = P(1+r/m)mt 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 A(365) = 100 000(1+0.005)365 =$617 465

The equivalent annual (normal) rate of interest compounded daily is

\$617 465 = 100 000(1+r/365)365

which works out to

r = 182.5 %

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.>     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.