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Is it Better to Buy or Rent?
Many expensive items, from cars to furniture can be either bought or
rented. Suppose your old (fill in the blank--car, refridgerator, TV) breaks
down and you need to get a new one. Suppose a new one (or a new/used one
in the case of a car) costs $1000 but you don't have $1000 handy, but
you do have $75 per month extra income.
You have a choice of either:
- Buying the item on your credit card at an interest rate of 3% per month.
You must pay the interest each month, and you can pay as much of the
principle (the amount you borrowed) as you like.
- Saving the $75 per month in the bank at 2% interest per year
until you have enough to pay cash.
- Renting the item.
Which is the best deal?
Getting Started
- How much will you have to pay total
over the next five years if you
buy the item on credit?
- How much rent would you be willing to pay? (That is, how cheap does
the rent have to be to make it better to rent than to buy?)
- Suppose you can resell the item for $150 at the end of five years
if you own it. How does this change your answer to the above?
- Suppose you could find a better credit card that only charges
2% per month. How does this change your answer to the above?
Going Deeper
How does the total amount you pay for a loan depend on the
interest rate? Can you find a formula for this amount? Can you
approximate this amount somehow (even if you can't get an exact
formula)? Approximate how much you have after 20 years if you
save 75 dollars per month at 2 percent interest.
How much does this change if the interest rate increases by 1 percent?
Communicated by the Chelsea High School Mathematics Department.
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