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 Question from Cheryl, a parent: Compounded interest daily on cd.....$1,000.00 at 2.53% for 6 months. How much will this CD earn? Cheryl, Let's start with something easier. Suppose the interest is 5%, compounded once a year and you want to know the value at the end of the year. Since the interest is 5% per year then at the end of the year you receive$1,000 plus 5% of $1,000 which is$1,000 + 0.05 × $1,000 =$1,000(1 + 0.05)

I'm not really interested in the value, just the method used to calculate it. If the value is $P and the interest rate for the period is r then the value at the end of the period is$P(1 + r)

Now back to your problem. The calculate is very much the same. If the interest rate is 2.53% which is 0.0253 then the daily rate is 0.0253/365 . Hence at the end of the first day the value is

$1,000(1 + 0.0253/365) That's is then the value at the beginning of the second day, thus it is$P at the beginning of the second day. Hence the value at the end of the second day is

$P(1 + r) =$1,000(1 + 0.0253/365)(1 + 0.0253/365) = $1,000(1 + 0.0253/365)2 That's is then the value at the beginning of the third day, thus it is$P at the beginning of the third day. Hence the value at the end of the third day is

$P(1 + r) =$1,000(1 + 0.0253/365)2(1 + 0.0253/365) = \$1,000(1 + 0.0253/365)3

I hope you see the pattern now. What is the value at the end of the 183rd day?

Penny

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