Deandre borrowed money from an online lending company to buy a camper.He took out a personal, amortized loan for $18,000, at an interest rate of 5.2%, with monthly payments for a term of 4 years.For each part, do not round any intermediate computations and round your final answers to the nearest cent.If necessary, refer to the list of financial formulas.(a) Find Deandre's monthly payment.$(b) If Deandre pays the monthly payment each month for the full term, find his total amount to repay the loan.$(c) If Deandre pays the monthly payment each month for the full term, find the total amount of interest he will pay.$

(a) To find Deandre's monthly payment, we use the formula for the monthly payment on an amortized loan:

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

where:

• $M$ is the monthly payment
• $P$ is the loan principal ($18,000)
• $r$ is the monthly interest rate (annual rate divided by 12)
• $n$ is the total number of payments (loan term in months)

First, we need to find the monthly interest rate:

$r = \frac{5.2\%}{12} = \frac{0.052}{12} = 0.0043333$

Next, we calculate the total number of payments:

$n = 4 \text{ years} \times 12 \text{ months/year} = 48 \text{ months}$

Now we can plug these values into the formula:

$M = \frac{18000 \cdot 0.0043333 \cdot (1 + 0.0043333)^{48}}{(1 + 0.0043333)^{48} - 1}$

First, calculate $(1 + 0.0043333)^{48}$:

$(1 + 0.0043333)^{48} \approx 1.221386$

Now, calculate the numerator:

$18000 \cdot 0.0043333 \cdot 1.221386 \approx 95.276$

And the denominator:

$1.221386 - 1 = 0.221386$

Finally, calculate the monthly payment:

$M = \frac{95.276}{0.221386} \approx 430.36$

So, Deandre's monthly payment is approximately $430.36.

(b) To find the total amount Deandre will repay over the term of the loan, we multiply the monthly payment by the total number of payments:

$\text{Total repayment} = M \times n = 430.36 \times 48 \approx 20657.28$

So, the total amount to repay the loan is approximately $20,657.28.

(c) To find the total amount of interest Deandre will pay, we subtract the loan principal from the total repayment amount:

$\text{Total interest} = \text{Total repayment} - P = 20657.28 - 18000 \approx 2657.28$

So, the total amount of interest he will pay is approximately $2,657.28.

(a) To find Deandre's monthly payment, we use the formula for the monthly payment on an amortized loan:

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

where:

• $M$ is the monthly payment
• $P$ is the loan principal ($18,000)
• $r$ is the monthly interest rate (annual rate divided by 12)
• $n$ is the total number of payments (loan term in months)

First, we need to find the monthly interest rate:

$r = \frac{5.2\%}{12} = \frac{0.052}{12} = 0.0043333$

Next, we calculate the total number of payments:

$n = 4 \text{ years} \times 12 \text{ months/year} = 48 \text{ months}$

Now, we can plug these values into the formula:

$M = \frac{18000 \cdot 0.0043333 \cdot (1 + 0.0043333)^{48}}{(1 + 0.0043333)^{48} - 1}$

First, calculate $(1 + 0.0043333)^{48}$:

$(1 + 0.0043333)^{48} \approx 1.221386$

Now, calculate the numerator:

$18000 \cdot 0.0043333 \cdot 1.221386 \approx 95.276$

And the denominator:

$1.221386 - 1 = 0.221386$

Finally, calculate the monthly payment:

$M = \frac{95.276}{0.221386} \approx 430.36$

So, Deandre's monthly payment is approximately $430.36.

(b) To find the total amount to repay the loan, we multiply the monthly payment by the total number of payments:

$\text{Total repayment} = M \times n = 430.36 \times 48 \approx 20657.28$

So, the total amount to repay the loan is approximately $20,657.28.

(c) To find the total amount of interest Deandre will pay, we subtract the loan principal from the total repayment amount:

$\text{Total interest} = \text{Total repayment} - P = 20657.28 - 18000 \approx 2657.28$

So, the total amount of interest Deandre will pay is approximately $2,657.28.

(a) To find Deandre's monthly payment, we use the formula for the monthly payment on an amortized loan:

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

where:

• $M$ is the monthly payment,
• $P$ is the loan principal ($18,000),
• $r$ is the monthly interest rate (annual rate divided by 12),
• $n$ is the total number of payments (loan term in months).

First, we need to find the monthly interest rate:

$r = \frac{5.2\%}{12} = \frac{0.052}{12} = 0.0043333$

Next, we calculate the total number of payments:

$n = 4 \text{ years} \times 12 \text{ months/year} = 48 \text{ months}$

Now, we can plug these values into the formula:

$M = \frac{18000 \cdot 0.0043333 \cdot (1 + 0.0043333)^{48}}{(1 + 0.0043333)^{48} - 1}$

First, calculate $(1 + 0.0043333)^{48}$:

$(1 + 0.0043333)^{48} \approx 1.221386$

Now, calculate the numerator:

$18000 \cdot 0.0043333 \cdot 1.221386 \approx 95.199$

And the denominator:

$1.221386 - 1 = 0.221386$

Finally, calculate the monthly payment:

$M = \frac{95.199}{0.221386} \approx 430.07$

So, Deandre's monthly payment is approximately $430.07.

(b) To find the total amount Deandre will repay over the term of the loan, we multiply the monthly payment by the number of payments:

$\text{Total repayment} = M \times n = 430.07 \times 48 \approx 20643.36$

So, the total amount to repay the loan is approximately $20,643.36.

(c) To find the total amount of interest Deandre will pay, we subtract the loan principal from the total repayment amount:

$\text{Total interest} = \text{Total repayment} - P = 20643.36 - 18000 \approx 2643.36$

So, the total amount of interest he will pay is approximately $2,643.36.