A woman borrows $1,000 on 1 January 2002 at 16% per annum simple interest. She pays $350 on 12 April 2002, $200 on 10 August 2002 and $400 on 3 October 2002. What is the balance due on 1 January 2003?
P = Po + Po*r*t = 1000 + 1000*0.16*1 = $1,160,
1160 - (350 + 200 + 400) = $210 Due on 1 Jan. 2003.
To find the balance due on 1 January 2003, we need to calculate the interest accumulated on the loan for the entire year of 2002 and subtract the payments made.
First, let's find the interest accumulated. The formula for simple interest is:
Interest = Principal * Rate * Time
In this case, the principal amount is $1,000, the rate is 16% per annum, and the time is 1 year. Plugging in these values into the formula, we can calculate the interest as follows:
Interest = $1,000 * 0.16 * 1 = $160
Next, we need to subtract the payments made throughout the year. The woman made three payments: $350 on 12 April 2002, $200 on 10 August 2002, and $400 on 3 October 2002.
Subtracting these payments from the interest accumulated:
$160 - $350 - $200 - $400 = $-790
The negative value indicates that the total payments exceeded the interest accumulated. Therefore, the balance due on 1 January 2003 is $790 owed to the woman.