How to find compound interest - PSAT Math

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Donna wants to deposit money into a certificate of deposit so that in exactly ten years, her investment will be worth $100,000. The interest rate of the CD is 7.885%, compounded monthly.

What should Donna's initial investment be, at minimum?

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The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set (monthly = 12 periods), and , and evaluate $A_{0}$ :

$100,000 = A_{0} \left ( 1+ \frac{0.07885}{12} \right )^{12 \cdot 10}$

$100,000 \approx A_{0} \left ( 1+0.0065708\right )^{120}$

$100,000 \approx A_{0} \left ( 1 .0065708\right )^{120}$

$100,000 \approx A_{0} \cdot 2.1944$

$A_{0} \approx 100,000 \div 2.1944$

$A_{0} \approx 45,569.99$

The correct response is $45,569.99.

On January 15, 2015, Philip deposited $10,000 in a certificate of deposit that returned interest at an annual rate of 8.125%, compounded monthly. How much will his certificate of deposit be worth on January 15, 2020?

Tap to see back →

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set $A_{0} = 10,000, r = 0.08125, N = 12$ (monthly = 12 periods), and , and evaluate :

$A = 10,000 \left ( 1+ \frac{0.08125}{12} \right )^{12 \cdot 5}$

$A \approx 10,000 \left ( 1.0067708\right )^{60}$

$A \approx 10,000 \cdot 1.499124$

$A \approx 1 4,991.24$

The CD will be worth $14,991.24.

Money is deposited in corporate bonds which yield 6.735% annual interest compounded monthly, and which mature after ten years. Which of the following responses comes closest to the percent by which the value of bonds increases?

Tap to see back →

The formula for compound interest is

$A = $A_{0}$\left ( 1+ $\frac{r}{N}$ \right $)^{Nt}$$

where is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

In the given scenario, , , and (monthly); substitute:

$A = $A_{0}$\left ( 1+ $\frac{0.06735}{12}$ \right $)^{12 \cdot 10}$$

$A \approx $A_{0}$\left ( 1+0.0056125 \right $)^{12 0}$$

$A \approx $A_{0}$\left ( 1 .0056125 \right $)^{12 0}$$

$A \approx $A_{0}$ \cdot 1.9574$

This meas that the final value of the bonds is about 1.96 times their initial value, or, equivalently, 96% greater than their initial value. Of the given responses, 95% comes closest.

Tom invests $\$15$ , in a savings account with an annual interest rate of . If his investment is compounded semiannually, how much interest does he earn after years?

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In order to find the interest earned, used the compound interest formula

$\text{Final Balance} = \text{Principal} \cdot (1+\frac{IR}{C})^{(\text{Time})(\text{C})}$

where represents the number of times the account is compounded each year, and represents the interest rate expressed as a decimal.

$=15,000\cdot(1+\frac{.06}{2})^{(2)(2)}$

$=15,000\cdot(1+.03)^{4}$

$=15,000\cdot(1.03)^{4}$

The account is worth $16882.63 after two years. Therefore Tom earns $1882.63 in interest.

Donna wants to deposit money into a certificate of deposit so that in exactly ten years, her investment will be worth $100,000. The interest rate of the CD is 7.885%, compounded monthly.

What should Donna's initial investment be, at minimum?

Tap to see back →

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set (monthly = 12 periods), and , and evaluate $A_{0}$ :

$100,000 = A_{0} \left ( 1+ \frac{0.07885}{12} \right )^{12 \cdot 10}$

$100,000 \approx A_{0} \left ( 1+0.0065708\right )^{120}$

$100,000 \approx A_{0} \left ( 1 .0065708\right )^{120}$

$100,000 \approx A_{0} \cdot 2.1944$

$A_{0} \approx 100,000 \div 2.1944$

$A_{0} \approx 45,569.99$

The correct response is $45,569.99.

On January 15, 2015, Philip deposited $10,000 in a certificate of deposit that returned interest at an annual rate of 8.125%, compounded monthly. How much will his certificate of deposit be worth on January 15, 2020?

Tap to see back →

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set $A_{0} = 10,000, r = 0.08125, N = 12$ (monthly = 12 periods), and , and evaluate :

$A = 10,000 \left ( 1+ \frac{0.08125}{12} \right )^{12 \cdot 5}$

$A \approx 10,000 \left ( 1.0067708\right )^{60}$

$A \approx 10,000 \cdot 1.499124$

$A \approx 1 4,991.24$

The CD will be worth $14,991.24.

Money is deposited in corporate bonds which yield 6.735% annual interest compounded monthly, and which mature after ten years. Which of the following responses comes closest to the percent by which the value of bonds increases?

Tap to see back →

The formula for compound interest is

$A = $A_{0}$\left ( 1+ $\frac{r}{N}$ \right $)^{Nt}$$

where is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

In the given scenario, , , and (monthly); substitute:

$A = $A_{0}$\left ( 1+ $\frac{0.06735}{12}$ \right $)^{12 \cdot 10}$$

$A \approx $A_{0}$\left ( 1+0.0056125 \right $)^{12 0}$$

$A \approx $A_{0}$\left ( 1 .0056125 \right $)^{12 0}$$

$A \approx $A_{0}$ \cdot 1.9574$

This meas that the final value of the bonds is about 1.96 times their initial value, or, equivalently, 96% greater than their initial value. Of the given responses, 95% comes closest.

Tom invests $\$15$ , in a savings account with an annual interest rate of . If his investment is compounded semiannually, how much interest does he earn after years?

Tap to see back →

In order to find the interest earned, used the compound interest formula

$\text{Final Balance} = \text{Principal} \cdot (1+\frac{IR}{C})^{(\text{Time})(\text{C})}$

where represents the number of times the account is compounded each year, and represents the interest rate expressed as a decimal.

$=15,000\cdot(1+\frac{.06}{2})^{(2)(2)}$

$=15,000\cdot(1+.03)^{4}$

$=15,000\cdot(1.03)^{4}$

The account is worth $16882.63 after two years. Therefore Tom earns $1882.63 in interest.

Donna wants to deposit money into a certificate of deposit so that in exactly ten years, her investment will be worth $100,000. The interest rate of the CD is 7.885%, compounded monthly.

What should Donna's initial investment be, at minimum?

Tap to see back →

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set (monthly = 12 periods), and , and evaluate $A_{0}$ :

$100,000 = A_{0} \left ( 1+ \frac{0.07885}{12} \right )^{12 \cdot 10}$

$100,000 \approx A_{0} \left ( 1+0.0065708\right )^{120}$

$100,000 \approx A_{0} \left ( 1 .0065708\right )^{120}$

$100,000 \approx A_{0} \cdot 2.1944$

$A_{0} \approx 100,000 \div 2.1944$

$A_{0} \approx 45,569.99$

The correct response is $45,569.99.

On January 15, 2015, Philip deposited $10,000 in a certificate of deposit that returned interest at an annual rate of 8.125%, compounded monthly. How much will his certificate of deposit be worth on January 15, 2020?

Tap to see back →

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set $A_{0} = 10,000, r = 0.08125, N = 12$ (monthly = 12 periods), and , and evaluate :

$A = 10,000 \left ( 1+ \frac{0.08125}{12} \right )^{12 \cdot 5}$

$A \approx 10,000 \left ( 1.0067708\right )^{60}$

$A \approx 10,000 \cdot 1.499124$

$A \approx 1 4,991.24$

The CD will be worth $14,991.24.

Money is deposited in corporate bonds which yield 6.735% annual interest compounded monthly, and which mature after ten years. Which of the following responses comes closest to the percent by which the value of bonds increases?

Tap to see back →

The formula for compound interest is

$A = $A_{0}$\left ( 1+ $\frac{r}{N}$ \right $)^{Nt}$$

where is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

In the given scenario, , , and (monthly); substitute:

$A = $A_{0}$\left ( 1+ $\frac{0.06735}{12}$ \right $)^{12 \cdot 10}$$

$A \approx $A_{0}$\left ( 1+0.0056125 \right $)^{12 0}$$

$A \approx $A_{0}$\left ( 1 .0056125 \right $)^{12 0}$$

$A \approx $A_{0}$ \cdot 1.9574$

This meas that the final value of the bonds is about 1.96 times their initial value, or, equivalently, 96% greater than their initial value. Of the given responses, 95% comes closest.

Tom invests $\$15$ , in a savings account with an annual interest rate of . If his investment is compounded semiannually, how much interest does he earn after years?

Tap to see back →

In order to find the interest earned, used the compound interest formula

$\text{Final Balance} = \text{Principal} \cdot (1+\frac{IR}{C})^{(\text{Time})(\text{C})}$

where represents the number of times the account is compounded each year, and represents the interest rate expressed as a decimal.

$=15,000\cdot(1+\frac{.06}{2})^{(2)(2)}$

$=15,000\cdot(1+.03)^{4}$

$=15,000\cdot(1.03)^{4}$

The account is worth $16882.63 after two years. Therefore Tom earns $1882.63 in interest.

Donna wants to deposit money into a certificate of deposit so that in exactly ten years, her investment will be worth $100,000. The interest rate of the CD is 7.885%, compounded monthly.

What should Donna's initial investment be, at minimum?

Tap to see back →

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set (monthly = 12 periods), and , and evaluate $A_{0}$ :

$100,000 = A_{0} \left ( 1+ \frac{0.07885}{12} \right )^{12 \cdot 10}$

$100,000 \approx A_{0} \left ( 1+0.0065708\right )^{120}$

$100,000 \approx A_{0} \left ( 1 .0065708\right )^{120}$

$100,000 \approx A_{0} \cdot 2.1944$

$A_{0} \approx 100,000 \div 2.1944$

$A_{0} \approx 45,569.99$

The correct response is $45,569.99.

On January 15, 2015, Philip deposited $10,000 in a certificate of deposit that returned interest at an annual rate of 8.125%, compounded monthly. How much will his certificate of deposit be worth on January 15, 2020?

Tap to see back →

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set $A_{0} = 10,000, r = 0.08125, N = 12$ (monthly = 12 periods), and , and evaluate :

$A = 10,000 \left ( 1+ \frac{0.08125}{12} \right )^{12 \cdot 5}$

$A \approx 10,000 \left ( 1.0067708\right )^{60}$

$A \approx 10,000 \cdot 1.499124$

$A \approx 1 4,991.24$

The CD will be worth $14,991.24.

Money is deposited in corporate bonds which yield 6.735% annual interest compounded monthly, and which mature after ten years. Which of the following responses comes closest to the percent by which the value of bonds increases?

Tap to see back →

The formula for compound interest is

$A = $A_{0}$\left ( 1+ $\frac{r}{N}$ \right $)^{Nt}$$

where is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

In the given scenario, , , and (monthly); substitute:

$A = $A_{0}$\left ( 1+ $\frac{0.06735}{12}$ \right $)^{12 \cdot 10}$$

$A \approx $A_{0}$\left ( 1+0.0056125 \right $)^{12 0}$$

$A \approx $A_{0}$\left ( 1 .0056125 \right $)^{12 0}$$

$A \approx $A_{0}$ \cdot 1.9574$

This meas that the final value of the bonds is about 1.96 times their initial value, or, equivalently, 96% greater than their initial value. Of the given responses, 95% comes closest.

Tom invests $\$15$ , in a savings account with an annual interest rate of . If his investment is compounded semiannually, how much interest does he earn after years?

Tap to see back →

In order to find the interest earned, used the compound interest formula

$\text{Final Balance} = \text{Principal} \cdot (1+\frac{IR}{C})^{(\text{Time})(\text{C})}$

where represents the number of times the account is compounded each year, and represents the interest rate expressed as a decimal.

$=15,000\cdot(1+\frac{.06}{2})^{(2)(2)}$

$=15,000\cdot(1+.03)^{4}$

$=15,000\cdot(1.03)^{4}$

The account is worth $16882.63 after two years. Therefore Tom earns $1882.63 in interest.

Donna wants to deposit money into a certificate of deposit so that in exactly ten years, her investment will be worth $100,000. The interest rate of the CD is 7.885%, compounded monthly.

What should Donna's initial investment be, at minimum?

Tap to see back →

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set (monthly = 12 periods), and , and evaluate $A_{0}$ :

$100,000 = A_{0} \left ( 1+ \frac{0.07885}{12} \right )^{12 \cdot 10}$

$100,000 \approx A_{0} \left ( 1+0.0065708\right )^{120}$

$100,000 \approx A_{0} \left ( 1 .0065708\right )^{120}$

$100,000 \approx A_{0} \cdot 2.1944$

$A_{0} \approx 100,000 \div 2.1944$

$A_{0} \approx 45,569.99$

The correct response is $45,569.99.

On January 15, 2015, Philip deposited $10,000 in a certificate of deposit that returned interest at an annual rate of 8.125%, compounded monthly. How much will his certificate of deposit be worth on January 15, 2020?

Tap to see back →

The formula for compound interest is

$A = A_{0}\left ( 1+ \frac{r}{N} \right )^{Nt}$

where $A_{0}$ is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

Set $A_{0} = 10,000, r = 0.08125, N = 12$ (monthly = 12 periods), and , and evaluate :

$A = 10,000 \left ( 1+ \frac{0.08125}{12} \right )^{12 \cdot 5}$

$A \approx 10,000 \left ( 1.0067708\right )^{60}$

$A \approx 10,000 \cdot 1.499124$

$A \approx 1 4,991.24$

The CD will be worth $14,991.24.

Money is deposited in corporate bonds which yield 6.735% annual interest compounded monthly, and which mature after ten years. Which of the following responses comes closest to the percent by which the value of bonds increases?

Tap to see back →

The formula for compound interest is

$A = $A_{0}$\left ( 1+ $\frac{r}{N}$ \right $)^{Nt}$$

where is the initial investment, is the interest rate expressed as the decimal equivalent, is the number of periods per year the interest is compounded, is the number of years, and is the final value of the investment.

In the given scenario, , , and (monthly); substitute:

$A = $A_{0}$\left ( 1+ $\frac{0.06735}{12}$ \right $)^{12 \cdot 10}$$

$A \approx $A_{0}$\left ( 1+0.0056125 \right $)^{12 0}$$

$A \approx $A_{0}$\left ( 1 .0056125 \right $)^{12 0}$$

$A \approx $A_{0}$ \cdot 1.9574$

This meas that the final value of the bonds is about 1.96 times their initial value, or, equivalently, 96% greater than their initial value. Of the given responses, 95% comes closest.

Tom invests $\$15$ , in a savings account with an annual interest rate of . If his investment is compounded semiannually, how much interest does he earn after years?

Tap to see back →

In order to find the interest earned, used the compound interest formula

$\text{Final Balance} = \text{Principal} \cdot (1+\frac{IR}{C})^{(\text{Time})(\text{C})}$

where represents the number of times the account is compounded each year, and represents the interest rate expressed as a decimal.

$=15,000\cdot(1+\frac{.06}{2})^{(2)(2)}$

$=15,000\cdot(1+.03)^{4}$

$=15,000\cdot(1.03)^{4}$

The account is worth $16882.63 after two years. Therefore Tom earns $1882.63 in interest.