Question 563742
person borrows $10,000
pays back loan in equal installments.
interest is 12% per year.
amount of repayments if:
annually = 1338.79
quarterly = 331.12
monthly = 110.11
weekly = 25.39


total paid with each method is:
annually = 1338.79 * 20 - 10000 = 16775.8
quarterly = 331.12 * 20 * 4 - 10000 = 16489.6
monthly = 110.11 * 20 * 12 - 10000 = 16426.4
weekly = 25.39 * 20 * 52 - 10000 = 16405.6


the cheapest of the four methods is paying every week.
this is because the balance goes down with each payment so the total interest paid becomes less.


here's an example:
loan is 10000
interest is 10% per year.
loan is paid off in one year.


yearly payments
each payment is 10100.
balance is 10000 * 1.10 = 10100 at the end of the year.
you make a payment of 10100 at the end of the year and the balance becomes 10100 - 10100 = 0.
total interest paid is 1 * 10100 - 10000 = 100.


semi-annual payments.
interest rate is 10% / 2 = 5% every 6 months.
each payment is 5378.04878.
balance is 10000 * 1.05 = 10500 at the end of 6 months.
you make a payment of 5378.04878 at the end of 6 months and the balance becomes 
10500 - 5378.04878 = 5121.95122
balance is 5121.95122 * 1.05 = 5378.04878 at the end of 12 months.
you make a payment of 5378.04878 at the end of 12 months and the balance becomes 5378.04878 - 5378.04878 = 0
total interest paid is equal to 2 * 5378.04878 - 10000 = 756.09756
total interest is less because the interest rate is being applied to the remaining balance and the remaining balance becomes less after each payment.
10% of 10000 = 100
5% of 10000 = 500 and then 5% of 5121.95122 = 256.09756 for a total interest of 756.09756