can youu pleasee help me with

Question

A bank features a savings account that has an annual percentage rate of % with interest compounded quarterly. Tom deposits $9,000 into the account.The account balance can be modeled by the exponential formula , where  is account value after  years ,  is the principal (starting amount),  is the annual percentage rate,  is the number of times each year that the interest is compounded.(A) What values should be used for , r, and ?

Answer 1

Hello Nurlan!

I'll try and help out with your problem!

This is the interest formula you provided:

A(t) = a*(1 + rk)^kt

This formula actually has an error in it. The "r" inside the parenthesis should be divided by "k", rather than being multiplied by "k".

So the correct interest formula is:

A(t) = a*(1 + (r / k))^kt

Now let's interpret each term in this formula...

1. A(t) : the final amount of money in the account after "t" years have passed
2. t : the amount of years that have passed since the initial investment
3. a : the original amount of money invested, sometimes called the "principal"
4. r : the annual interest rate. If interest is compounded "quarterly", then each time interest is applied, one-forth of this rate is applied. This is why the "r" term is divided by "k" in our equation.
5. k : the number of times per year that interest is compounded. If it is applied quarterly then this should equal 4. If we compound monthly, then this would be 12, or if compounded annually this would equal 1, etc.

Based on this understanding of all the terms, we can see that...

1. a = $9000
2. r = 0.027
3. k = 4

I hope that helps!

--Zach