Question 724057
Hey,

So for this one, we need to create a formula for calculating the amount. A normal compounded interest formula looks like this:

A = B ( 1 + r ) ^n 

Where A is the ending amount of money, in this case $1000. B is the beginning amount of money, in this case x because we don't know. Little r is the rate, in this case .08 (or 8%). Little n is the number of years the money is in the bank, in this case 10 years. This would work, HOWEVER, the interest is compounded quarterly, which means 4 times a year. Therefore the formula is change to look like this:

A = B ( 1 + r/t ) ^ (n)(t) 

Where everything is the same except that we divide the rate (r) by the number of times a year the interest is made (t) and then instead of just taking that amount to the exponent of n, we need to first multiply n by the number of times per year (t). So this is what this problem would look like:

$1,000 = x ( 1 + .08/4 ) ^ (10)(4) 

First we solve what is in the parentheses:

 1 + .08/4 => 1 + .02 => 1.02 

Then we multiply the exponents together:

 (10)(4) => 40 

Then we take 1.02 ^ 40 => 2.208... 

Now we have to isolate the x so we can solve for it. In order to do this, we need to get rid of the 2.208 by dividing both sides by 2.208 :

 $1000/2.208 = x (2.208)/2.208 => 452.8985..... = x 

And now we have the answer.

If we deposit around $453 into a bank with compound interest of 8% quarterly, we will have $1000 after 10 years. 

Again the answer is $453. 

I hope this helps!