2) Solve For \[$ R \$\] Where \[$ P = \$18,000.00 \$\], \[$ I = \$5,500.00 \$\], And \[$ T = 48 \$\] Months.$\[ R = \\] (Change To Percent And Round To The Tenth's Place)1. What Is The Total Amount You Would

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Understanding the Problem

In this article, we will solve for the interest rate in a loan where the principal amount, interest, and time are given. We will use the formula for simple interest, which is:

A=P(1+rt){ A = P(1 + rt) }

where:

  • A is the total amount
  • P is the principal amount
  • r is the interest rate
  • t is the time in years

However, in this problem, we are given the interest in dollars, not as a percentage. Therefore, we will need to convert the interest rate from dollars to a percentage.

Given Values

  • Principal amount (P): $18,000.00
  • Interest (i): $5,500.00
  • Time (t): 48 months

Converting Time from Months to Years

Since the time is given in months, we need to convert it to years. There are 12 months in a year, so:

t=48 months=4812=4 years{ t = 48 \text{ months} = \frac{48}{12} = 4 \text{ years} }

Solving for the Interest Rate

Now that we have the time in years, we can use the formula for simple interest to solve for the interest rate:

A=P(1+rt){ A = P(1 + rt) }

We are given the total amount (A) as the principal amount (P) plus the interest (i):

A=P+i{ A = P + i }

Substituting this into the formula, we get:

P+i=P(1+rt){ P + i = P(1 + rt) }

Simplifying the equation, we get:

i=Prt{ i = Prt }

Now, we can substitute the given values into the equation:

5500=18000×r×4{ 5500 = 18000 \times r \times 4 }

Solving for r, we get:

r=550018000×4{ r = \frac{5500}{18000 \times 4} }

r=550072000{ r = \frac{5500}{72000} }

r=0.07639{ r = 0.07639 }

Converting the Interest Rate to a Percentage

To convert the interest rate to a percentage, we multiply by 100:

r=0.07639×100{ r = 0.07639 \times 100 }

r=7.639%{ r = 7.639\% }

Rounding to the Tenth's Place

Finally, we round the interest rate to the tenth's place:

r=7.6%{ r = 7.6\% }

Conclusion

In this article, we solved for the interest rate in a loan where the principal amount, interest, and time were given. We used the formula for simple interest and converted the interest rate from dollars to a percentage. The final answer is:

r=7.6%{ r = 7.6\% }

Additional Information

  • The interest rate is 7.6% per year.
  • The total amount is $18,000.00 + $5,500.00 = $23,500.00.
  • The time is 48 months, which is equivalent to 4 years.

References

Related Topics

Q: What is the formula for simple interest?

A: The formula for simple interest is:

A=P(1+rt){ A = P(1 + rt) }

where:

  • A is the total amount
  • P is the principal amount
  • r is the interest rate
  • t is the time in years

Q: How do I convert the interest rate from dollars to a percentage?

A: To convert the interest rate from dollars to a percentage, you multiply the interest rate by 100:

r=iP×100{ r = \frac{i}{P} \times 100 }

where:

  • i is the interest in dollars
  • P is the principal amount

Q: What is the difference between simple interest and compound interest?

A: Simple interest is calculated only on the principal amount, while compound interest is calculated on both the principal amount and any accrued interest.

Q: How do I calculate the total amount using the formula for simple interest?

A: To calculate the total amount using the formula for simple interest, you can use the following steps:

  1. Plug in the values for P, r, and t into the formula: A=P(1+rt){ A = P(1 + rt) }
  2. Simplify the equation: A=P+Prt{ A = P + Prt }
  3. Calculate the total amount: A=P+i{ A = P + i }

Q: What is the time in years equivalent to 48 months?

A: The time in years equivalent to 48 months is 4 years.

Q: How do I round the interest rate to the tenth's place?

A: To round the interest rate to the tenth's place, you can use the following steps:

  1. Calculate the interest rate: r=iP{ r = \frac{i}{P} }
  2. Multiply the interest rate by 100 to convert it to a percentage: r=iP×100{ r = \frac{i}{P} \times 100 }
  3. Round the interest rate to the tenth's place: r=7.6%{ r = 7.6\% }

Q: What is the total amount in the example problem?

A: The total amount in the example problem is $23,500.00.

Q: What is the interest rate in the example problem?

A: The interest rate in the example problem is 7.6% per year.

Q: How do I use the formula for simple interest to solve for the interest rate?

A: To use the formula for simple interest to solve for the interest rate, you can use the following steps:

  1. Plug in the values for P, i, and t into the formula: i=Prt{ i = Prt }
  2. Simplify the equation: i=Prt{ i = Prt }
  3. Calculate the interest rate: r=iPt{ r = \frac{i}{Pt} }

Q: What is the principal amount in the example problem?

A: The principal amount in the example problem is $18,000.00.

Q: What is the interest in the example problem?

A: The interest in the example problem is $5,500.00.

Q: How do I convert the time from months to years?

A: To convert the time from months to years, you can divide the number of months by 12:

t=4812=4 years{ t = \frac{48}{12} = 4 \text{ years} }

Q: What is the final answer to the example problem?

A: The final answer to the example problem is:

r=7.6%{ r = 7.6\% }