You wish to finance the purchase of some living room furniture for $$ \$ 3,800 $$. A bank offers an APR of $$ 16.75 \% $$ on a 36 -month installment loan. After first using Table $$ 13-1 $$ to find the finance charge, calculate your monthly payment. Select one: a. $$ \$ 105.56 $$ b. $$ \$ 135.01 $$ c. $$ \$ 123.10 $$ d. $$ \$ 149.10 $$

Question

UpStudy AI · Accepted Answer

To solve this problem, we need to follow these steps:

1. **Calculate the finance charge using the APR and the loan amount.**
2. **Determine the total amount to be repaid.**
3. **Calculate the monthly payment by dividing the total amount by the number of months.**

### Step 1: Calculate the Finance Charge

The finance charge can be calculated using the formula:

$$
\text{Finance Charge} = \text{Loan Amount} \times \text{APR} \times \text{Time}
$$

Where:
- Loan Amount = $$ 3800 $$
- APR = $$ 16.75\% = 0.1675 $$
- Time = $$ 3 $$ years = $$ 36 $$ months

Now, we can calculate the finance charge.

### Step 2: Calculate the Total Amount to be Repaid

The total amount to be repaid is given by:

$$
\text{Total Amount} = \text{Loan Amount} + \text{Finance Charge}
$$

### Step 3: Calculate the Monthly Payment

The monthly payment can be calculated as:

$$
\text{Monthly Payment} = \frac{\text{Total Amount}}{\text{Number of Months}}
$$

Now, let's perform the calculations.

First, we will calculate the finance charge.

$$
\text{Finance Charge} = 3800 \times 0.1675 \times 3
$$

Let's calculate this value.
Calculate the value by following steps:
- step0: Calculate:
  $$3800\times 0.1675\times 3$$
- step1: Multiply the terms:
  $$636.5\times 3$$
- step2: Multiply the numbers:
  $$1909.5$$
The finance charge is calculated to be $$ 1909.5 $$.

### Step 2: Calculate the Total Amount to be Repaid

Now, we can calculate the total amount to be repaid:

$$
\text{Total Amount} = 3800 + 1909.5 = 5709.5
$$

### Step 3: Calculate the Monthly Payment

Now, we can calculate the monthly payment:

$$
\text{Monthly Payment} = \frac{5709.5}{36}
$$

Let's calculate this value.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{5709.5}{36}$$
- step1: Convert the expressions:
  $$\frac{\frac{11419}{2}}{36}$$
- step2: Multiply by the reciprocal:
  $$\frac{11419}{2}\times \frac{1}{36}$$
- step3: Multiply the fractions:
  $$\frac{11419}{2\times 36}$$
- step4: Multiply:
  $$\frac{11419}{72}$$
The monthly payment is calculated to be approximately $$ 158.60 $$.

However, this value does not match any of the provided options. Let's double-check the calculations and ensure we are using the correct method to find the finance charge based on the APR and the loan term.

### Re-evaluating the Finance Charge

The finance charge is typically calculated using a finance charge table or a specific formula for installment loans. Given that we need to use Table 13-1, we would typically look up the finance charge for a loan of $$ \$3,800 $$ at an APR of $$ 16.75\% $$ for $$ 36 $$ months.

Since we don't have access to Table 13-1, let's assume a standard method for calculating the monthly payment using the formula for an installment loan:

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

Where:
- $$ M $$ = monthly payment
- $$ P $$ = principal (loan amount)
- $$ r $$ = monthly interest rate (APR / 12)
- $$ n $$ = number of payments (months)

### Step 1: Calculate Monthly Interest Rate

$$
r = \frac{0.1675}{12}
$$

### Step 2: Calculate Monthly Payment

Now, we can substitute $$ P = 3800 $$, $$ r $$, and $$ n = 36 $$ into the formula to find $$ M $$. Let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{0.1675}{12}$$
- step1: Convert the expressions:
  $$\frac{\frac{67}{400}}{12}$$
- step2: Multiply by the reciprocal:
  $$\frac{67}{400}\times \frac{1}{12}$$
- step3: Multiply the fractions:
  $$\frac{67}{400\times 12}$$
- step4: Multiply:
  $$\frac{67}{4800}$$
Calculate or simplify the expression $$ 3800 * (0.1675 / 12) * (1 + (0.1675 / 12))^36 / ((1 + (0.1675 / 12))^36 - 1) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{3800\left(\frac{0.1675}{12}\right)\left(1+\left(\frac{0.1675}{12}\right)\right)^{36}}{\left(\left(1+\left(\frac{0.1675}{12}\right)\right)^{36}-1\right)}$$
- step1: Remove the parentheses:
  $$\frac{3800\left(\frac{0.1675}{12}\right)\left(1+\left(\frac{0.1675}{12}\right)\right)^{36}}{\left(1+\left(\frac{0.1675}{12}\right)\right)^{36}-1}$$
- step2: Divide the terms:
  $$\frac{3800\left(\frac{0.1675}{12}\right)\left(1+\frac{67}{4800}\right)^{36}}{\left(1+\left(\frac{0.1675}{12}\right)\right)^{36}-1}$$
- step3: Add the numbers:
  $$\frac{3800\left(\frac{0.1675}{12}\right)\left(\frac{4867}{4800}\right)^{36}}{\left(1+\left(\frac{0.1675}{12}\right)\right)^{36}-1}$$
- step4: Divide the terms:
  $$\frac{3800\left(\frac{0.1675}{12}\right)\left(\frac{4867}{4800}\right)^{36}}{\left(1+\frac{67}{4800}\right)^{36}-1}$$
- step5: Add the numbers:
  $$\frac{3800\left(\frac{0.1675}{12}\right)\left(\frac{4867}{4800}\right)^{36}}{\left(\frac{4867}{4800}\right)^{36}-1}$$
- step6: Divide the terms:
  $$\frac{3800\times \frac{67}{4800}\left(\frac{4867}{4800}\right)^{36}}{\left(\frac{4867}{4800}\right)^{36}-1}$$
- step7: Multiply:
  $$\frac{\frac{1273\times 4867^{36}}{24\times 4800^{36}}}{\left(\frac{4867}{4800}\right)^{36}-1}$$
- step8: Subtract the numbers:
  $$\frac{\frac{1273\times 4867^{36}}{24\times 4800^{36}}}{\frac{4867^{36}-4800^{36}}{4800^{36}}}$$
- step9: Multiply by the reciprocal:
  $$\frac{1273\times 4867^{36}}{24\times 4800^{36}}\times \frac{4800^{36}}{4867^{36}-4800^{36}}$$
- step10: Rewrite the expression:
  $$\frac{1273\times 4867^{36}}{24\times 4800^{36}}\times \frac{24^{36}\times 200^{36}}{4867^{36}-4800^{36}}$$
- step11: Reduce the numbers:
  $$\frac{1273\times 4867^{36}}{4800^{36}}\times \frac{24^{35}\times 200^{36}}{4867^{36}-4800^{36}}$$
- step12: Rewrite the expression:
  $$\frac{1273\times 4867^{36}}{24^{36}\times 200^{36}}\times \frac{24^{35}\times 200^{36}}{4867^{36}-4800^{36}}$$
- step13: Reduce the numbers:
  $$\frac{1273\times 4867^{36}}{24\times 200^{36}}\times \frac{200^{36}}{4867^{36}-4800^{36}}$$
- step14: Rewrite the expression:
  $$\frac{1273\times 4867^{36}}{24\times 200^{36}}\times \frac{8^{36}\times 25^{36}}{4867^{36}-4800^{36}}$$
- step15: Rewrite the expression:
  $$\frac{1273\times 4867^{36}}{8\times 3\times 200^{36}}\times \frac{8^{36}\times 25^{36}}{4867^{36}-4800^{36}}$$
- step16: Reduce the numbers:
  $$\frac{1273\times 4867^{36}}{3\times 200^{36}}\times \frac{8^{35}\times 25^{36}}{4867^{36}-4800^{36}}$$
- step17: Rewrite the expression:
  $$\frac{1273\times 4867^{36}}{3\times 8^{36}\times 25^{36}}\times \frac{8^{35}\times 25^{36}}{4867^{36}-4800^{36}}$$
- step18: Reduce the numbers:
  $$\frac{1273\times 4867^{36}}{3\times 8}\times \frac{1}{4867^{36}-4800^{36}}$$
- step19: Multiply the fractions:
  $$\frac{1273\times 4867^{36}}{24\left(4867^{36}-4800^{36}\right)}$$
- step20: Multiply:
  $$\frac{1273\times 4867^{36}}{24\times 4867^{36}-24\times 4800^{36}}$$
The monthly interest rate $$ r $$ is calculated to be approximately $$ 0.013958 $$.

Using this value, the monthly payment $$ M $$ is calculated to be approximately $$ 135.01 $$.

### Final Answer

Thus, the monthly payment for the loan is approximately $$ 135.01 $$.

The correct option is:
**b. $$ \$ 135.01 $$**.
The monthly payment is approximately \$135.01. **b. \$135.01**

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Arithmetic Questions