Question

5. Imagine you have $1,000 in the bank account. You have decided to spend $100 for a new cloth. Consider three methods to finance this purchase. First, you can withdraw $100 from your bank account and pay for the purchase up front; second you can charge your purchases to your credit card and set- tle the debt a year from now, thus the credit card bill to be paid next year is $110, assuming 10% interest rate. Your last option is to charge $100 on your credit card with no intention of ever paying off the debt. Instead, you make a $10 interest payments to the finance company every year forever. Which payment scheme do you prefer and why? For any purposes (borrow- ing, saving), consider 10% interest rate.

Answer includes all the necessary graphs.

Answer 1

Since they all have the same present value $100 in each case, the options are all equally desirable. To verify this, let us assume that you start with $1000 in the bank and compute your financial status 1 year from now under each of the three options.

If you pay for the clothes up front, your bank balance falls to $900, which earns $90 interest (continuing assume 10% interest rate) over the course of the year. one year from today your balance is $990.

If you charge to your credit card and pay next year, you leave $1000 in the bank, which grows to $1100 over the course of the year. You then withdraw $110 to pay the credit card bill, and your balance is again $990.

Finally, under the plan where you charge to your credit card and never pay the debt, your bank balance increases to $1100 , of which you withdraw $10 to make your first annual interest payment, leaving $1090. Of this, there is $100 that you dare never withdraw , since the income that it yields is necessary to make your future credit card payments of $10 per year. this leaves you with a usable balance of $990 , exactly in the first two cases.

In other words, all three plans leave you equally wealthy, as we know they must.