Question 563742: a person borrows $10000 and agrees to repay the loan in equal instalments over 20 years. interest is 12% per annum on any money owing
A) what is the amount of each repayment, if the repayment are made
i) annually, ii) quarterly, iii) monthly, iv) weekly
B) which is the cheapest of the four methods of repayment in (A)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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
|
|
|
