Question

Given a loan amount P, an annual interest rate r, and the length of the loan in years, find the monthly payment R necessary to pay off the loan by completing parts a through c. Represent the number of monthly payments by n. Amount Rate Time $60,000 5% 25 years a. Calculate $P left(1 + frac{r}{12} ight)^n$ and call this number A. A = oxed{} (Round to two decimal places as needed.) b. Calculate $frac{left(1 + frac{r}{12} ight)^n - 1}{frac{r}{12}}$ and call this number B. B = oxed{} (Round to two decimal places as needed.) c. Let $R = frac{A}{B}$ The monthly payment necessary to pay off the loan is R = $oxed{}$. (Round up to the nearest cent.)

          Given a loan amount P, an annual interest rate r, and the length of the loan in years, find the monthly payment R necessary to pay off the loan by completing parts a through c. Represent the number of monthly payments by n.
Amount
Rate
Time
$60,000
5%
25 years
a. Calculate $P left(1 + frac{r}{12}
ight)^n$ and call this number A.
A = oxed{} (Round to two decimal places as needed.)
b. Calculate $frac{left(1 + frac{r}{12}
ight)^n - 1}{frac{r}{12}}$ and call this number B.
B = oxed{} (Round to two decimal places as needed.)
c. Let $R = frac{A}{B}$
The monthly payment necessary to pay off the loan is R = $oxed{}$.
(Round up to the nearest cent.)

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$Given a loan amount P, an annual interest rate r, and the length of the loan in years, find the monthly payment R necessary to pay off the loan by completing parts a through c. Represent the number of monthly payments by n. Amount Rate Time 60,000 5% 25 years a. CalculateP left(1 + fracr12 ight)^nand call this number A. A = oxed (Round to two decimal places as needed.) b. Calculatefracleft(1 + fracr12 ight)^n - 1fracr12and call this number B. B = oxed (Round to two decimal places as needed.) c. LetR = fracABThe monthly payment necessary to pay off the loan is R =oxed. (Round up to the nearest cent.)$

Added by Jennifer H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Maitreya E

06/24/2022

Step 1

05}{12}\right)^{12 \times 25} \] \[ A = 60000 \times 1.417^{300} \] \[ A = 60000 \times 6049.12 \] \[ A = 362946720 \] Show more…

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Given a loan amount P, an annual interest rate r, and the length of the loan in years, find the monthly payment R necessary to pay off the loan by completing parts a through c. Represent the number of monthly payments by n. Amount $60,000 Rate 5% Time 25 years a. Calculate P(1 + r/12)^n and call this number A. A = (Round to two decimal places as needed.) b. Calculate [(1 + r/12)^n - 1] / (r/12) and call this number B. B = (Round to two decimal places as needed.) c. Let R = A/B. The monthly payment necessary to pay off the loan is R = $ (Round up to the nearest cent.)

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Transcript

00:01 Hi there in this question it is given that the principal amount p is equal to $60 ,000.

00:05 The interest rate is 5 % and the number of years is 25 years.

00:11 And here in a part we have to find capital a equal to p multiplied by 1 plus r divided by 12 to the part n.

00:19 In the b part we have to find capital b is equal to 1 plus r divided by 12 whole power n minus 1 divided by r divided by r divided by 12.

00:31 And in the c part, we have to find r is equal to a divided by b, where r is the amount that is necessary to, that, the monthly payment that is necessary to pay off the loan.

00:42 So let's see how we'll do this.

00:45 So in the first case, we have a is equal to p multiplied by 1 plus r divided by 12 to the power n.

00:51 That is this is equal to 60 ,000 multiplied by 1 plus 5 divided by 12 to the power 25.

01:01 So here we'll be having this is equal to 60 ,000 multiplied by 1 .417 to the power 25.

01:14 That is equal to 60 ,000 multiplied by 6 ,049 .12.

01:25 And this product will be equal to, this is equal to 362.

01:35 946 956.

01:37 So we got this value here.

01:39 So a is equal to 362 -946 -9 -56.

01:45 So we got the value of a here.

01:48 This is the required value of a...

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