Question

Suppose you want to buy an item whose current price is $1000. You consider the following two options.

• Finance the item now, i.e. take out a loan for $1000 and buy the item immediately. The loan company charges 9% interest, compounded monthly, and they offer you a one year loan with payments due at the end of each month.

• Create a sinking fund now and make monthly deposits (at the end of each month) for one year, then purchase the item one year from now, right when you make your twelfth deposit. Assume your bank offers 2% interest, compounded monthly.

*** On all questions below, be sure to show complete work, including the setup of a partial geometric sum if necessary. (Plug and chug into book formulas will receive little if any credit.) Do your work as if you do not have a calculator, except that you should convert final answers to amounts in dollars and cents.

(a) If you take out the loan, what is the total amount of money you pay back to the loan company? How much of it is interest?

(b) Assume the item’s popularity is decreasing and its price in one year will be only 95% of the current price. What is the total amount of money you have to deposit into your sinking fund to make the purchase? How much does your bank contribute in the form of interest?

(c) How much money would you save if you saved up for the item in your sinking fund rather than buying it on credit with the loan above? (Ignore inflation and other real life complications.)

(d) What are some reasons people might take out the loan for the item, even though they end up paying more?

Answer 1