Daily Compounded CD Rate?

Question

Investment Amount: $4597.00
Issue Date: 10/07/2006
Maturity Date: 5/07/2007
Term: 7 months
Interest Rate: 6.767%
APY: 7.0%

How much will I earn at the end of the term?

Answer 1

I'm assuming that this is a homework problem -- because it doesn't match up with the real world.

First -- let me give you the solution. Daily compounded CDs use an "Actual/360 Accrual Method." This means that to get the daily rate, you divide the yearly interest rate by 360 and then compound the actual number of days. Yes -- I agree it is stupid not to use 365, but it is what is done.

Using this method, the APR (or APY) is calculated as follows -- whgere R is the Interest Rate:

(1+R/360)^365-1 = 7.101%

It looks like the person who said that the APR is equal to 7.0% divided by 365 instead of 360. This is not the right way to do it.

The formula for finding the interest is:

Interest = Amount * (1+R/360)^(# Periods)

Since the number of periods is the number of days between 10/7 and 5/7 -- we have to count them. It is 212 days -- so the right amount at the end of the period is:

4597*(1+.06767/360)^212 = 4783.87

This means you earned 186.87 in interest

If you make the same mistake of dividing by 365 instead of 360 to get the daily rate, then the answer is 184.26.

Note that Koko made a different mistake. He was right that you should be able to use the APR and use the fraction of the year that you are invested as the power. However, he assumed that since it was seven months, that the right fraction to use is 7/12. But remember we are compounding daily -- so the right fraction is 212/365.

Answer 2

It's actually really easy, the APY is the real interest rate (already factored in the daily compounding), so for one year, you would get $321.79, but for your term which is 7 month, you would get $187.71

Answer 3

The correct algebraic method is as follows:

If the APY (annual percentage yield) is 7%, then after 212 days your sum becomes
4597 x 1.07^ (212/365) = $4781.25,
which means an interest of $184.25

It seems I got the same answer as Taranto (within 1cent)without counting the year as 360 days.After you get paid, please let me know who was correct.