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Determine the exact simple interest on 1,000,000 invested for the period from October 24,1987 to January 7, 1990; if the rate of interest is 17%.

What I've tried:

October 24, 1987 to October 24, 1988 -> 365 days

October 24, 1998 to October 24, 1989 -> 365 days

October 24, 19 1989 to January 7, 1990 -> 75 days

I = Pin = $(1,000,000)(\frac{0.17}{365})(365 + 365 + 365) = 374,931.51$

But the answer should be: 93,785.079.

Any ideas what I got wrong? Thank you~

Key Flex
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Jayce
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  • Some banks consider that a year is 360 days instead of 365. I don't know if it's the case here, but just saying ... Also, you probably want to use compound interest, am I right? So you need to raise numbers to a power, instead of adding/multiplying. – Matti P. Feb 01 '19 at 12:49
  • @MattiP. The question states "exact" so I used 365 days instead of 360. Then it also states "simple interest" so I used the formula for S.I. Sadly, I didn't get the right answer. – Jayce Feb 01 '19 at 13:06

2 Answers2

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Your answer is correct.

$$\mbox{October } 24-31 \mbox{ is } 7 \mbox{ days}\ \ \ \ \ \ \ \ \ \ \ \ \ \mbox{Total days in }1987 \mbox{ is }68 \mbox{ days} $$

$$\mbox{November } 30 \mbox{ days}\ \ \ \ \ \ \ \ \ \ \ \ \ \mbox{Total days in }1988 \mbox{ is }366 \mbox{ days} $$

$$\mbox{December } 31 \mbox{ days}\ \ \ \ \ \ \ \ \ \ \ \ \ \mbox{Total days in }1989 \mbox{ is }365 \mbox{ days} $$

$$\mbox{October } 1-7 \mbox{ is } 7 \mbox{ days}\ \ \ \ \ \ \ \ \ \ \ \ \ \mbox{Total days in }1990 \mbox{ is }7 \mbox{ days} $$

So, Number of interest days $=68+366+365=806$

Number of days from $1987$ to $1990$ is $=365+366+365+365=1461$

So, $I=1,000,000(0.17)\left(\dfrac{806}{1461}\right)=93,785.079$

Key Flex
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This problem involves exact simple interest in a period of more than a year and covers year 1988 which is a leap year (366days/year). Hence the calculation for each year must be separated and then summed up. Hence

Oct. 24 to Oct. 31, 1987 is 7 days

Nov. 1 to Dec 31, 1987 is 30+31=61 days

Total number of days for year 1987 is 7+61=68 days

Total number of days for year 1988 (leap year) is 366 days

Total number of days for year 1989 (ordinary year) is 365 days

Total number of days for year 1990 is (Jan 1 to Jan 7) 7 days

I(1987) = 1,000,000(0.17)(68/365) = 31,671.23

I(1988) = 1,000,000(0.17)(366/366) = 170,000.00

I(1989) = 1,000,000(0.17)(365/365) = 170,000.00

I(1990) = 1,000,000(0.17)(7/365) = 3,260.27

I(total) = 31,671.23+170,000(2)+3,260.27 = 374,931.50

Note: The answer for this problem could not be lower than the interest for a year because this involves more than two years. The interest for a year is 170,000.00 already as shown in my calculation above, for more than two years its should have an interest of more than the double of a years interest.

Joe Karlo Seva
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    As it’s currently written, your answer is unclear. Please [edit] to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. – Community Oct 06 '21 at 04:22
  • Your answer could be improved by stating your main assumption about the time interval corresponding to the given interest rate: is it one year, or is it the four years including the investment period? – Saeed Oct 06 '21 at 06:34