Simple Troubles

SIMPLE TROUBLES.

Why don't banks pay simple interest? We can see some of the difficulties with simple interest by considering the case of an enterprising engineering student named Jane. Before starting college Jane saved $2,000 to buy a computer for her school work. But when she settled into her dorm, she realized that

she could get by with the publicly available computer labs and
if she waited to buy a computer she could get a better one for the same money.

So Jane deposited her $2000 in a bank account which paid 4% interest per year.

Nine months later, at the end of the academic year, Jane withdrew her money with the intention of finally buying a computer. Suppose the bank paid simple interest. How much interest would Jane have earned? (Check your answer.)

The problem is that Jane did not leave her money in the bank for an entire year. The bank might well argue that she should earn no interest! But a fairer thing to do would be to prorate the interest. In other words, interest should be paid in proportion to how long the money was left in the back. Since she left her money in the bank for 3/4 of a year, she should receive 3/4 of the yearly interest, or

3
	year 4% per year $2000 = $60.
4

Interest should be prorated according to the length of time the principal is deposited.

Continuing with our story, Jane bought a computer at the end of the year and used it to earn some money over the summer. She returned to college with the larger sum of $2500 which she immediately put into a savings account at the same 4% yearly interest rate. She intended to leave it there for a year. Had she done that, her account would have been worth

$2500 + (4%

$2500) = $2500 + $100 = $2600

at the end of that year, assuming the bank paid simple interest. But Jane had a clever idea. After six months she went to the bank and withdrew her money. At that point her account had accumulated

1
	(4%) $2500 = $50.
2

in interest since her principal was on deposit for half of a year. The minute she withdrew the money, she re-deposited it. Her new principal was $2550. This earned interest for 6 more months, and at the end of the year Jane withdrew

$2550 + (1/2)

(4%)

$2550 = $2550 + $51 = $2601.

By withdrawing and re-depositing her money, Jane finished the year with an extra dollar!

This effect is called compounding. Compounding is explored on the next page.

From the point of view of a depositor, simple interest is unfair. As the bank pays interest, your balance grows and you should be earning interest on the entire balance, not just the original balance. The page "Real Life Interest" explains current banking practices and how to compute how much interest you really get from a bank. Meanwhile, as an exercise to check your understanding, we ask what would have happened if Jane had gone to the bank 4 times during the year to withdraw and re-deposit her money.

Exercise

Fill in the following table which shows what would have happened if Jane had gone to the bank every 1/4 year to withdraw and re-deposit her money. Note that 1/4 of 4% is 1%, which makes the calculations simple. Assume the bank rounds to the nearest cent.

Fill in the interest earned (the blank which says "FILL IN") and then click on the check button. This will check your answer and automatically fill in the ending balance and next beginning balance. Repeat until the table is complete.