Suppose you invest \$10 at 10.2% per annum compounded annually. How many years would it take for your investment to grow to \$15 000?

Question

I'am solving a simlar equation to this and just trying to figure out how they did it?

the only part I don't understand is how they got the number.... 1.102

15000 = 10(1.102)n ¬1 mark 1500 = 1.102n

Answer 1

The 1.102 comes from two places.

First, "%" means hundredths. If you see "10.2%", that really means $\frac{10.2}{100}$, which is 0.102.

Second, if your money is earning 10.2% interest annually, that means that at the end of the year, the bank takes your balance, multiplies it by 10.2%—that is, by 0.102—and hands you that much more in interest.

Your new balance after a year is equal to your old balance, plus the interest. Or, in symbols:

new balance = old balance + (old balance × 0.102)

or written another way:

new balance = (old balance × 1) + (old balance × 0.102)

which adds up to:

new balance = old balance × (1 + 0.102)

And that $1 + 0.102$ is there the 1.102 came from.

Okay?