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