top of page # Support Group

Public·12 members

# Compound Interest Common Core Algebra 2 Homework

## Compound Interest Common Core Algebra 2 Homework

Compound interest is the interest that is calculated based on the initial principal and the accumulated interest of previous periods. It is different from simple interest, where interest is only calculated based on the initial principal. Compound interest is a common topic in Algebra 2, and it is related to the Common Core State Standards for Mathematics (CCSSM) . In this article, we will review some of the concepts and formulas related to compound interest, and provide some examples and exercises for homework.

## Compound Interest Formula

The formula for calculating compound interest is:

## Compound Interest Common Core Algebra 2 Homework

Compound Interest = Amount - Principal

Where the amount is given by:

A = P(1 + r/n)

Where:

• A = amount

• P = principal

• r = annual interest rate (as a decimal)

• n = number of times interest is compounded per year

• t = time (in years)

This formula can be used to find the amount, the principal, the interest rate, the number of compounding periods, or the time, depending on what information is given and what is unknown.

## Examples

Here are some examples of how to use the compound interest formula:

If you invest \$5000 in an account that pays 8% annual interest compounded quarterly, how much money will you have after 10 years?

To solve this problem, we need to use the formula for the amount:

A = P(1 + r/n)

Plugging in the given values, we get:

A = 5000(1 + 0.08/4)

A = 5000(1.02)

A = 5000(2.208)

A = 11040

• Therefore, you will have \$11,040 after 10 years.

If you borrow \$10,000 from a bank that charges 12% annual interest compounded monthly, how much interest will you pay after 5 years?

To solve this problem, we need to use the formula for the compound interest:

Compound Interest = Amount - Principal

We also need to use the formula for the amount:

A = P(1 + r/n)

Plugging in the given values, we get:

A = 10000(1 + 0.12/12)

A = 10000(1.01)

A = 10000(1.816)

A = 18160

Therefore, the amount after 5 years is \$18,160. To find the compound interest, we subtract the principal from the amount:

Compound Interest = 18160 - 10000

Compound Interest = 8160

• Therefore, you will pay \$8,160 in interest after 5 years.

If you deposit \$2000 in an account that pays 6% annual interest compounded daily, how long will it take for your money to double?

To solve this problem, we need to use the formula for the time:

t = ln(A/P) / n[ln(1 + r/n)]

We also need to know that when the money doubles, the amount is equal to twice the principal:

A = 2P

Plugging in the given values, we get:

t = ln(2P/P) / (365)[ln(1 + 0.06/365)]

t = ln(2) / (365)[ln(1.000164)]

t = 0.693 / (365)(0.000164)

t = 11.55

• Therefore, it will take about 11.55 years for your money to double.

## Homework Exercises

• If you invest \$3000 in an account that pays 10% annual interest compounded semiannually, how much money will you have after 8 years?

• If you borrow \$15,000 from a bank that charges 9% annual interest compounded quarterly, how much interest will you pay after 3 years?

• If you deposit \$1000 in an account that pays 5% annual interest compounded continuously, how long will it take for your money to triple?

A = 3000(1 + 0.10/2)

A = 3000(1.05)

A = 3000(2.406)

A = 7218

• Therefore, you will have \$7,218 after 8 years.

A = 15000(1 + 0.09/4)

A = 15000(1.0225)

A = 15000(1.297)

A = 19455

Therefore, the amount after 3 years is \$19,455. To find the compound interest, we subtract the principal from the amount:

Compound Interest = 19455 - 15000

Compound Interest = 4455

• Therefore, you will pay \$4,455 in interest after 3 years.

t = ln(A/P) / r

We also need to know that when the money triples, the amount is equal to three times the principal:

A = 3P

Plugging in the given values, we get:

t = ln(3P/P) / 0.05

t = ln(3) / 0.05

t = 22.18

• Therefore, it will take about 22.18 years for your money to triple.

## Compound Interest Applications

Compound interest has many applications in real life, such as saving, investing, borrowing, and growing. Here are some examples of how compound interest can be used to model different situations:

Saving: If you want to save money for a future goal, such as buying a car, going to college, or retiring, you can use compound interest to estimate how much money you need to deposit now or how much you need to save each month. For example, if you want to buy a car that costs \$25,000 in 5 years, and you can earn 4% annual interest compounded monthly in a savings account, you can use the formula for the amount to find out how much you need to deposit now:

A = P(1 + r/n)

Plugging in the given values, we get:

25000 = P(1 + 0.04/12)

25000 = P(1.0033)

25000 = P(1.221)

P = 25000 / 1.221

P = 20473.13

• Therefore, you need to deposit \$20,473.13 now to buy the car in 5 years.

Investing: If you want to invest money in a business, a stock, or a fund that pays a certain rate of return, you can use compound interest to estimate how much money you will earn or how long it will take for your investment to grow. For example, if you invest \$10,000 in a stock that pays 15% annual interest compounded quarterly, you can use the formula for the time to find out how long it will take for your investment to double:

t = ln(A/P) / n[ln(1 + r/n)]

We also need to know that when the investment doubles, the amount is equal to twice the principal:

A = 2P

Plugging in the given values, we get:

t = ln(2P/P) / (4)[ln(1 + 0.15/4)]

t = ln(2) / (4)[ln(1.0375)]

t = 0.693 / (4)(0.0367)

t = 4.71

• Therefore, it will take about 4.71 years for your investment to double.

Borrowing: If you want to borrow money from a bank, a credit card company, or a friend that charges a certain rate of interest, you can use compound interest to estimate how much money you will have to pay back or how long it will take for you to pay off your debt. For example, if you borrow \$5000 from a friend that charges 6% annual interest compounded monthly, and you agree to pay \$100 per month until the debt is paid off, you can use the formula for the number of compounding periods to find out how many months it will take for you to pay off your debt:

n = ln(A/P) / t[ln(1 + r/n)]

We also need to know that when the debt is paid off, the amount is equal to zero:

A = 0

Plugging in the given values, we get:

n = ln(0/5000) / (100)[ln(1 + 0.06/12)]

n = - / (100)[ln(1.005)]

n = - / (100)(0.00497)

n = - / 0.497

n = -

• This means that it is impossible for you to pay off your debt with this payment plan. You will either have to increase your monthly payment or negotiate a lower interest rate with your friend.

Growing: If you want to model the growth of a population, a bacteria culture, or a tumor that grows at a certain rate per unit time, you can use compound interest to estimate how large or how small the population or the mass will be after a certain period of time. For example, if a bacteria culture has an initial mass of 2 grams and grows at a rate of 20% per hour compounded hourly, you can use the formula for the amount to find out how large the mass will be after 12 hours:

A = P(1 + r/n)

Plugging in the given values, we get:

A = 2(1 + 0.20/1)

A = 2(1.20)

A = 2(8.916)

A = 17.832

• Therefore, the mass will be 17.832 grams after 12 hours.

## Conclusion

Compound interest is a powerful concept that can be used to model various situations involving money, growth, or decay. By using the compound interest formula and its variations, we can calculate the amount, the principal, the interest rate, the number of compounding periods, or the time for any compound interest problem. We can also apply compound interest to real life scenarios such as saving, investing, borrowing, and growing. Compound interest is an important topic in Algebra 2 and in the Common Core State Standards for Mathematics . By mastering compound interest, we can improve our mathematical skills and our financial literacy.