Question

Addison currently has an account balance of $1,737.83. She opened the account 11 years ago with a deposit of $1,334.62. If the interest compounds semi-annually, what is the interest rate on the account?
1.2%
2.4%
4.1%
7.7%

Answer 1

Anyone?!

Answer 2

First of all, how many times did the interest compound?
By how much did it the account increase?

Answer 3

Use \[
I = Pr^t
\]\(I\) is the amount of interest (increase in the account ammount)
\(P\) is principle (initial amount in account\).
\(r\) the interest rate (you want to solve for this\).
\(t\) how many ties it compounded.

Answer 4

It says it compounds semi-annually. Soo.. 1737.83 = (1334.92)(R)(22)?

Answer 5

Well, for one, it's \(r^t\) meaning \(r\) to the power of \(t\). It is not \(r\) times \(t\).
Secondly, \(I\) is not the final amount. It is the change in the amount.
So that makes it the final amount minus the initial amount.

Answer 6

Oh, okay. So rather, it's (403.21) = (1334.92)R^22?

Answer 7

If it is (403.21) = (1334.92)R^22, I'm not sure what steps to take to solve that.. I don't know how to work with R being raised by 22.

Answer 8

You will have to use a calculator.

Answer 9

Remember that: \[
(a^b)^{c} = a^{bc}
\]If we let \(c=1/b\) then we have: \[
(a^b)^{1/b} = a^{b/b} = a^1 =a
\]

So to get rid of the \(22\) exponent. Take both sides to the power of \(22\).

Answer 10

To the power of \(1/22\) I mean.

Answer 11

@GeorgeB2838 Make sense?

Answer 12

Actually, do you mean I raise each side to the power of 1/22?

Answer 13

I'm afraid I still don't understand the steps to take to solve this equation (403.21) = (1334.92)R^22. Do I divide 1334.92 from 403.21 first, and then raise both sides to the power of 1/22?

Answer 14

Do division first.

When you are isolating a variable, usually you do things opposite of the order of operationans. (adding/subtracting first, multiplying dividing second, then exponents).