01 July 2011

Quiz answers Part I

This will take a couple of entries. We'll take on the first two quiz questions today, and address the others in due time. 

1.      Suppose you had $100 in a savings account and the interest rate was 2% per year. After 5 years, how much do you think you would have in the account if you left the money to grow?
a.       More than $102
b.      Exactly $102
c.       Less than $102
d.      Do not know

OK, so you go to the bank and deposit $100 at an interest rate of 2%. What does that mean? It means that you leave the money there and in a year you will have 2% more than you started with. Simple math version: $100 + ($100 * .2%) = $100 + $2 = $102.

But the question says that you leave the money in the bank for five years. It’s pretty easy to work through that. We’ve already done Year 1.

Year 1  $100 + ($100 * .02)  = $102.  This can also be expressed as $100 * 1.02 = $102.

Year 2  $102 * 1.02 = $104.04. This is where we start to see the magic of compound interest!

Year 3  $104.40 * 1.02 = $106.12 (We’ll round to the nearest penny.)

Year 4  $106.49 * 1.02 = $108.24

Year 5  $108.61 * 1.02 = $110.41

So, if you leave $100 in the bank earning 2% in annual interest, in five years you can withdraw $110.41, which is more than $102.

2.      Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year. After 1 year, how much would you be able to buy with the money in this account?
a.       More than today
b.      Exactly the same as today
c.       Less than today
d.      Do not know

We have a good start towards answering this one. We know how to calculate how much money is in a savings account after one year. However, this time the interest rate is 1%.

$100 * 1.01 = $101

However, we are dealing with inflation here. Inflation means that prices are rising. This can happen for a variety of reasons, but usually the cost of the underlying goods is rising for one reason or another. The relevant piece of information here is that inflation is 2%. That means that $100 worth of stuff on January 1 would cost $102 to buy one year later.

Year 1 inflation $100 * 1.02 = $102

This means that even though you saved money and had it earning 1% per year, inflation has outpaced you. At the end of the year you would need $102 to buy all of that stuff, but you only have $101. Which sucks, but also means that the answer is ‘less than today.’ 

That's enough for today. There will be more answers tomorrow!

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