Step-by-Step Guidance for Compound Interest Problems in College Algebra

Q1. Brenda invests $4,310 in a savings account with a fixed annual interest rate of 5%, compounded 5 times per year. What will the account balance be after 6 years?

Background

Topic: Compound Interest

This question tests your understanding of how to calculate the future value of an investment using the compound interest formula, given the principal, interest rate, compounding frequency, and time.

Key formula:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ = future value (account balance after $t$ years)

• $P$ = principal (initial investment)

• $r$ = annual interest rate (as a decimal)

• $n$ = number of times interest is compounded per year

• $t$ = number of years

Step-by-Step Guidance

1. Identify the known values: $P = 4310$, $r = 0.05$, $n = 5$, $t = 6$.

2. Plug these values into the compound interest formula: $A = 4310 \left(1 + \frac{0.05}{5}\right)^{5 \times 6}$.

3. Calculate $\frac{0.05}{5}$ to find the periodic interest rate.

4. Calculate $5 \times 6$ to find the total number of compounding periods.

Try solving on your own before revealing the answer!

Final Answer: $5,831.56$

$A = 4310 \left(1 + 0.01\right)^{30}$

After calculating the exponent and multiplying by the principal, the account balance after 6 years is $5,831.56$.

Q2. Lisa invests $6,330 in a savings account with a fixed annual interest rate of 8%, compounded 7 times per year. What will the account balance be after 4 years?

Background

Topic: Compound Interest

This question is similar to Q1, focusing on the effect of a higher interest rate and more frequent compounding periods.

Key formula:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $P = 6330$

• $r = 0.08$

• $n = 7$

• $t = 4$

Step-by-Step Guidance

1. Write out the formula with the values: $A = 6330 \left(1 + \frac{0.08}{7}\right)^{7 \times 4}$.

2. Calculate $\frac{0.08}{7}$ for the periodic interest rate.

3. Calculate $7 \times 4$ for the total number of compounding periods.

4. Set up the expression for the exponent and multiplication, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Final Answer: $8,721.22$

$A = 6330 \left(1 + 0.01143\right)^{28}$

After calculating the exponent and multiplying by the principal, the account balance after 4 years is $8,721.22$.

Q3. Jessica invests $2,510 in a retirement account with a fixed annual interest rate of 6% compounded 4 times per year. What will the account balance be after 15 years?

Background

Topic: Compound Interest

This question tests your ability to apply the compound interest formula over a longer time period, which demonstrates the power of compounding.

Key formula:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $P = 2510$

• $r = 0.06$

• $n = 4$

• $t = 15$

Step-by-Step Guidance

1. Substitute the values into the formula: $A = 2510 \left(1 + \frac{0.06}{4}\right)^{4 \times 15}$.

2. Calculate $\frac{0.06}{4}$ for the periodic interest rate.

3. Calculate $4 \times 15$ for the total number of compounding periods.

4. Set up the exponent and multiplication, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Final Answer: $6,072.50$

$A = 2510 \left(1 + 0.015\right)^{60}$

After calculating the exponent and multiplying by the principal, the account balance after 15 years is $6,072.50$.

Q4. Maria invests $6,314 in a savings account with a fixed annual interest rate of 6%, compounded 6 times per year. What will the account balance be after 8 years?

Background

Topic: Compound Interest

This question is similar to previous ones, but with different values for principal, rate, compounding frequency, and time.

Key formula:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $P = 6314$

• $r = 0.06$

• $n = 6$

• $t = 8$

Step-by-Step Guidance

1. Substitute the values into the formula: $A = 6314 \left(1 + \frac{0.06}{6}\right)^{6 \times 8}$.

2. Calculate $\frac{0.06}{6}$ for the periodic interest rate.

3. Calculate $6 \times 8$ for the total number of compounding periods.

4. Set up the exponent and multiplication, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Final Answer: $10,099.16$

$A = 6314 \left(1 + 0.01\right)^{48}$

After calculating the exponent and multiplying by the principal, the account balance after 8 years is $10,099.16$.