# CAHSEE Math 3.3 Number Sense

Number Sense Drill 3 Problem 3. How much interest will Warren have earned in three years?

 Algebra PercentsWord Problems CAHSEE Math Number Sense Language English Language Number Sense Percentages

### Transcript

00:22

How much interest will he have earned in three years?

00:25

00:32

00:36

...in this case we have SIMPLE interest which means that the rate is compounded at the end

00:40

of the year and returned to its owner to be spent on... hair growth formula... or whatever.

00:45

Simple makes life much... simpler.

00:48

So we have 3 iterations we have to do if we want to use the brute force method...

00:52

First we take 1200 and multiply it by 1.04

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Note the zero in there -- it's 4% interest, not 40

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So 1200 times 1.04 gives you 1248.

01:03

That's how much is in there after the first year -- 48 bucks in interest income for doing...

01:07

a whole lotta nothing.

01:09

No wonder the rich get richer.

01:11

Since the interest is simple, we just multiply that simple interest number by 3 and we get

01:15

3 times 48, or 144.

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1200 plus 144 is 1344 and voila -- the answer is C.

01:23

But quick gut check for advanced students -- what if the interest had been retained

01:26

in the bank account and NOT spent on hair growth formula?

01:30

Do the computation again for year 2 and we have 1248 times 1.04 and that gives us 1298, roughly.

01:37

Now we do it a third time... 1298 times 1.04 is approximately 1350.

01:42

Interestingly, it's a fair \$6 BETTER than the simple interest formula -- that

01:47

is, by leaving the money in the bank, we made \$6 more in interest.

01:50

Yeah, it's a latte today, but it adds up.

01:53

And if we'd been given this keep-the-money-in-the-bank question to resolve after, say, 27 years of compounding.

01:59

...we'd take the entire exam time doing it by this brute force method... so we need

02:03

another system -- a simple...ish formula.

02:06

We could have gotten the same answer by multiplying the 1200 times the

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quantity (1+.04) to the 3rd power.

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That is, we'd calculated 1.04 to the 3rd, then multiply

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that number by the initial \$1200 principal.

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Muuuuch easier when many years are involved.

02:23

Oh the wealth a whole lot of sitting around on your duff can create.