For the following exercises, use the compound interest...

For the following exercises, use the compound interest formula, $A(t)=P\left(1+\frac{r}{n}\right)^{n t}$ Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded semiannually, had an initial deposit of $\$ 9,000$ and was worth $\$ 13,373.53$ after 10 years.

For the following exercises, use the compound interest formula, $A(t)=P\left(1+\frac{r}{n}\right)^{n t}$
Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded semiannually, had an initial deposit of $\$ 9,000$ and was worth $\$ 13,373.53$ after 10 years.

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Key Concepts

Compound Interest

Compound interest is a financial concept where interest is not only earned on the initial principal but also on the accumulated interest from previous periods. This principle is used to calculate the future value of an investment or loan by applying the interest repeatedly over multiple periods.

Compounding Frequency

Compounding frequency refers to how often the interest is applied to the principal within a given time period. In the compound interest formula, varying the number of compounding periods per year (n) affects the growth of the investment, making it an important factor in calculating the final account balance.

Solving for the Interest Rate

In many financial problems, it is necessary to determine the interest rate given the initial principal, final amount, and compounding details. This involves rearranging the compound interest formula and often using logarithms to solve for the rate, applying both algebraic skills and an understanding of exponential growth.

Transcript

00:01 All right, so we have an equation.

00:02 A of t is equal to p times 1 plus r of rent to the nt, and we are going to use this to find the interest rate for a account that was competent semi -annually and had an initial deposit of $9 ,000, and it's now worth $13 ,373 .53 .53 after 10 years.

00:21 Okay, so a lot of different numbers.

00:22 And i drew them out over here.

00:24 And basically, what we have to do is plug them in, and we're going to be solving for the interest rate, which is just r.

00:31 So we were given that, you know, a is this number, the final amount.

00:37 P was the initial that we put in.

00:39 N is 2.

00:40 N, the reason why it's 2 is because it said that it was compounded semi -annually, meaning it's twice a year, which is why n would be 2.

00:48 And then t, which is time is this 10 years.

00:51 So all we're going to do is plug all these into the equation, and we're just going to solve for r.

00:56 Pretty straightforward.

00:57 So we have 13373 .53 .53 is equal to 9 ,000 times 1 plus trying to find r over, what was it, 2? to the, okay, so to the two times pretty straightforward.

01:37 T was 10, and that's it.

01:44 Just making sure i got everything.

01:45 All right...

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