4.2% means 0.042 .
4.2% more than some amount is 1.042 of it.
Interest compounded annually means that a year after you deposit some money
into your bank account, the bank looks to see how much of your money has been
there for a year, and they add 4.2% of that into your account. Another way to
look at it is that they change the balance in your account, from the amount it was
a year ago, to 1.042 of that amount. That's right. They just give you free money !
Why that's so good is: Now the new amount in your account is 1.042 of
the amount you originally deposited, and after another year, they'll give you
another 4.2% of that larger amount. Then you'll have (1.042)² = about
8.6% more than your original deposit, 2 years earlier.
At the end of any number of years ... call it 't' years ... the amount in your
account is the amount you deposited, multiplied by (1.042)^'t' power.
If you just put some money into this particular bank, and forget about it
and never touch it, you'll have double the amount in 17 years.
Now we can go and take care of Rhonda.
She put $3000 into a new account at the the bank, and then she forgot
about it and never touched it. How much is in that account after 't' years ?
The amount that's in that account at any time is called the 'balance'.
How much is it after 't' years ?
Balance = 3,000 (1.042)^'t' power .
