Jessie purchased a notebook for $10,500 using a credit card. She

considers two repayment plans.
i She makes the minimum monthly payment of $300 offered by the
credit card and no other charges are applicable.
ii She makes monthly payments of $900 and no other charges are applicable.
Compare the above plans. Which is better for Jessie if the interest is 4% per annum? And, how long would it take for Jessie to settle the repayment if she were to adopt plan (i) for three years and then plan (ii) thereafter?

To compare the two repayment plans, we need to calculate the total cost Jessie would incur under each plan and see which one is lower.

Plan (i):
Under this plan, Jessie makes the minimum monthly payment of $300. Assuming an interest rate of 4% per annum, the interest charged each month can be calculated by dividing the annual interest rate by 12 (months). Thus, the monthly interest rate would be 4% / 12 = 0.33%.

To determine the duration required to settle the repayment under Plan (i) for three years, we multiply the number of years by 12 (months) to get the total number of months, which is 3 years * 12 months = 36 months.

Now, we can calculate the total cost under Plan (i) using the formula for the compound interest on a decreasing principal:

P = R * (1 - (1 + I)^(-N)) / I

Where:
P = Principal amount (total cost)
R = Monthly repayment amount ($300)
I = Monthly interest rate (0.33%)
N = Number of months (36)

Calculating P for Plan (i):
P = 300 * (1 - (1 + 0.0033)^(-36)) / 0.0033
P ≈ $11,006.71

Plan (ii):
Under this plan, Jessie makes monthly payments of $900. Since there are no other charges applicable, the total cost under Plan (ii) would simply be the sum of 36 payments of $900 each.

Calculating P for Plan (ii):
P = 900 * 36
P = $32,400

Comparing the two plans:
We can see that Plan (ii) has a total cost of $32,400, while Plan (i) has a total cost of $11,006.71. Therefore, Plan (i) is better for Jessie as it would result in a lower total cost.

Calculating the time required to settle the repayment under Plan (i) for three years and then Plan (ii) thereafter:
Since Jessie is adopting Plan (i) for three years, the remaining repayment period can be calculated as 36 months minus 36 months (3 years), resulting in zero remaining months for Plan (i).

For Plan (ii), since Jessie is adopting it thereafter, the repayment period would be the remaining time starting from month 37 until the total cost is fully paid off.

Therefore, under Plan (i) for three years and Plan (ii) thereafter, the total repayment duration would be 36 months for Plan (i) and the additional time required for Plan (ii) until the total cost is fully paid off.