A loan of $15,000 is taken at 7% per annum simple interest on April 7, and it is due exactly 7 months later (on November 7). Using exact time in days (April 7 to November 7 = 214 days) and a 365-day year, what is the total amount to be repaid (in $)?

Introduction / Context:
This is a simple interest “exact time” problem. Even though the duration is stated as seven months, the problem explicitly guides us to use exact days from April 7 to November 7. Under exact simple interest, we use t = (number of days) / 365. Then interest I = P * r * t, and total amount repaid A = P + I. This tests correct time conversion and careful substitution without compounding.

Given Data / Assumptions:

• Principal, P = $15,000
• Annual simple interest rate, r = 7% per annum = 0.07
• Start date: April 7
• Due date: November 7 (7 months later)
• Exact days between dates = 214 days
• Exact time method: t = 214/365 years

Concept / Approach:
Use exact simple interest:
I = P * r * t t = 214/365 Then compute total repayment:
A = P + I

Step-by-Step Solution:
t = 214/365 I = 15000 * 0.07 * (214/365) First compute: 15000 * 0.07 = 1050 So, I = 1050 * (214/365) I ≈ 615.52 (rounded to cents) A = 15000 + 615.52 = 15615.52

Verification / Alternative check:
If you used a rough 7/12 year estimate, interest would be close to 612.50, which is very near the exact-days result. The exact-days method gives a slightly different number because the actual day count is 214/365 ≈ 0.5863 years.

Why Other Options Are Wrong:
$14,615.52 and $13,615.52 incorrectly reduce principal by $1,000 or $2,000. $16,615.52 adds an extra $1,000 not justified by the interest. $15,500 is too low for 214 days at 7% on $15,000.

Common Pitfalls:
Using 7 months as 7/12 without considering exact days when asked, using 360-day year when 365 is specified, or accidentally compounding monthly.

Final Answer:
The total amount to be repaid is $15,615.52.