Question

terest rate find the annual interest rate.
t = 2 years

1. i = $562.50, p = $1500, t = 5 years

t = 18 months

1. i = $160, p = $2000, t = 8 months

Explanation:

Problem 16:

Step1: Recall the simple interest formula

The simple interest formula is \( I = P \times r \times t \), where \( I \) is the interest, \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal), and \( t \) is the time in years. We need to solve for \( r \), so we can rearrange the formula to \( r=\frac{I}{P\times t} \).

Step2: Identify the given values

We are given \( I = \$562.50 \), \( P = \$1500 \), and \( t = 5 \) years.

Step3: Substitute the values into the formula

Substitute \( I = 562.50 \), \( P = 1500 \), and \( t = 5 \) into \( r=\frac{I}{P\times t} \):
\[
r=\frac{562.50}{1500\times5}
\]

Step4: Calculate the denominator

First, calculate \( 1500\times5 = 7500 \).

Step5: Calculate the rate

Now, divide \( 562.50 \) by \( 7500 \):
\[
r=\frac{562.50}{7500}=0.075
\]

Step6: Convert to percentage

To convert the decimal to a percentage, multiply by 100: \( 0.075\times100 = 7.5\% \).

Step1: Recall the simple interest formula and adjust for time in years

The simple interest formula is \( I = P \times r \times t \), where \( t \) is in years. We have \( t = 8 \) months. Since there are 12 months in a year, \( t=\frac{8}{12}=\frac{2}{3} \) years. We need to solve for \( r \), so \( r=\frac{I}{P\times t} \).

Step2: Identify the given values

We are given \( I = \$160 \), \( P = \$2000 \), and \( t=\frac{2}{3} \) years.

Step3: Substitute the values into the formula

Substitute \( I = 160 \), \( P = 2000 \), and \( t=\frac{2}{3} \) into \( r=\frac{I}{P\times t} \):
\[
r=\frac{160}{2000\times\frac{2}{3}}
\]

Step4: Calculate the denominator

First, calculate \( 2000\times\frac{2}{3}=\frac{4000}{3} \).

Step5: Calculate the rate

Now, divide \( 160 \) by \( \frac{4000}{3} \). Dividing by a fraction is the same as multiplying by its reciprocal:
\[
r = 160\times\frac{3}{4000}=\frac{480}{4000}=0.12
\]

Step6: Convert to percentage

Multiply by 100 to get the percentage: \( 0.12\times100 = 12\% \).

Answer:

The annual interest rate is \( 7.5\% \).

Problem 18: