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Use the appropriate formula to find the amortization payment (in )
you would need to make each month, at interest compounded monthly,
to pay off a loan of in 3 years. (Round your answer to the
hearest cent.)

Ask by Lambert Reyes. in the United States

Mar 21,2025

Question

File Edit Format View Help
Use the appropriate formula to find the amortization payment (in )
you would need to make each month, at interest compounded monthly,
to pay off a loan of in 3 years. (Round your answer to the
hearest cent.)

Ask by Lambert Reyes. in the United States

Mar 21,2025

UpStudy AI · Accepted Answer

To find the amortization payment, we can use the formula for monthly payments on a loan:

$$ M = \frac{P \times r \times (1 + r)^n}{(1 + r)^n - 1} $$

Where:
- $$ M $$ is the monthly payment
- $$ P $$ is the principal amount (initial loan amount)
- $$ r $$ is the monthly interest rate (annual interest rate divided by 12)
- $$ n $$ is the number of payments (total number of months)

Given:
- Principal amount ($$ P $$) = $8,500
- Annual interest rate = 24%
- Compounded monthly
- Loan duration = 3 years = 36 months

First, we need to calculate the monthly interest rate ($$ r $$):

$$ r = \frac{24\%}{12} = 2\% $$

Now, we can substitute the values into the formula to find the monthly payment ($$ M $$):

$$ M = \frac{8500 \times 0.02 \times (1 + 0.02)^{36}}{(1 + 0.02)^{36} - 1} $$

Let's calculate the monthly payment using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{8500\times 0.02\left(1+0.02\right)^{36}}{\left(1+0.02\right)^{36}-1}$$
- step1: Add the numbers:
  $$\frac{8500\times 0.02\times 1.02^{36}}{\left(1+0.02\right)^{36}-1}$$
- step2: Add the numbers:
  $$\frac{8500\times 0.02\times 1.02^{36}}{1.02^{36}-1}$$
- step3: Convert the expressions:
  $$\frac{8500\times 0.02\left(\frac{51}{50}\right)^{36}}{1.02^{36}-1}$$
- step4: Convert the expressions:
  $$\frac{8500\times 0.02\left(\frac{51}{50}\right)^{36}}{\left(\frac{51}{50}\right)^{36}-1}$$
- step5: Multiply:
  $$\frac{170\times \frac{51^{36}}{50^{36}}}{\left(\frac{51}{50}\right)^{36}-1}$$
- step6: Subtract the numbers:
  $$\frac{170\times \frac{51^{36}}{50^{36}}}{\frac{51^{36}-50^{36}}{50^{36}}}$$
- step7: Evaluate the power:
  $$\frac{\frac{17\times 51^{36}}{10^{35}\times 5^{36}}}{\frac{51^{36}-50^{36}}{50^{36}}}$$
- step8: Multiply by the reciprocal:
  $$\frac{17\times 51^{36}}{10^{35}\times 5^{36}}\times \frac{50^{36}}{51^{36}-50^{36}}$$
- step9: Rewrite the expression:
  $$\frac{17\times 51^{36}}{10^{35}\times 5^{36}}\times \frac{10^{36}\times 5^{36}}{51^{36}-50^{36}}$$
- step10: Reduce the numbers:
  $$\frac{17\times 51^{36}}{5^{36}}\times \frac{10\times 5^{36}}{51^{36}-50^{36}}$$
- step11: Rewrite the expression:
  $$\frac{17\times 51^{36}}{5^{36}}\times \frac{5\times 2\times 5^{36}}{51^{36}-50^{36}}$$
- step12: Reduce the numbers:
  $$17\times 51^{36}\times \frac{2\times 5}{51^{36}-50^{36}}$$
- step13: Multiply:
  $$\frac{17\times 51^{36}\times 10}{51^{36}-50^{36}}$$
- step14: Multiply:
  $$\frac{170\times 51^{36}}{51^{36}-50^{36}}$$
The monthly payment needed to pay off the loan of $8,500 in 3 years at 24% interest compounded monthly is approximately $333.48.
The monthly amortization payment is approximately \$333.48.

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Use the appropriate formula to find the amortization payment (in )
you would need to make each month, at interest compounded monthly,
to pay off a loan of in 3 years. (Round your answer to the
hearest cent.)

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File Edit Format View Help Use the appropriate formula to find the amortization payment (in ) you would need to make each month, at interest compounded monthly, to pay off a loan of in 3 years. (Round your answer to the hearest cent.)

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File Edit Format View Help
Use the appropriate formula to find the amortization payment (in )
you would need to make each month, at interest compounded monthly,
to pay off a loan of in 3 years. (Round your answer to the
hearest cent.)