What Would The Monthly Payment Be?3) Solve For $p$ Where $i = \$1850.00$, $r = 4.2\%$, $t = 36$ Months.$p = \qquad$What Is The Total You Would Have To Repay The Bank?What Would The Monthly Payment Be?

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Introduction

When it comes to borrowing money, understanding the monthly payment is crucial in making informed decisions. In this article, we will delve into the world of mathematics and explore how to calculate the monthly payment using a simple formula. We will also discuss the importance of considering interest rates, repayment periods, and total amounts borrowed.

The Formula:

The formula to calculate the monthly payment is:

p = P [ i(1 + i)^t ] / [ (1 + i)^t – 1]

Where:

  • p = monthly payment
  • P = principal loan amount (the initial amount borrowed)
  • i = monthly interest rate (annual interest rate divided by 12)
  • t = number of payments (the number of months the loan is for)

Solving for pp

Let's use the given values to solve for pp:

  • i=$1850.00i = \$1850.00 (this is the monthly interest rate, not the principal loan amount)
  • r=4.2%r = 4.2\% (this is the annual interest rate, not the monthly interest rate)
  • t=36t = 36 months (this is the number of payments)

First, we need to convert the annual interest rate to a monthly interest rate:

i = r / 12 = 4.2 / 12 = 0.0035

Now, we can plug in the values into the formula:

p = P [ i(1 + i)^t ] / [ (1 + i)^t – 1]

However, we are given the value of ii, not PP. To find the total amount borrowed (PP), we need to use the formula:

P = p [ (1 + i)^t – 1 ] / [ i(1 + i)^t ]

But we don't know the value of pp yet. Let's rearrange the formula to solve for PP:

P = p / [ i(1 + i)^t ]

Now, we can plug in the values:

P = p / [ 0.0035(1 + 0.0035)^36 ]

To find the value of pp, we need to use the formula:

p = P [ i(1 + i)^t ] / [ (1 + i)^t – 1 ]

But we don't know the value of PP yet. Let's plug in the values:

p = P / [ (1 + 0.0035)^36 – 1 ]

Now, we have two equations and two unknowns. We can solve for PP and pp using substitution or elimination. Let's use substitution:

P = p / [ 0.0035(1 + 0.0035)^36 ]

p = P / [ (1 + 0.0035)^36 – 1 ]

Substituting the first equation into the second equation, we get:

p = (p / [ 0.0035(1 + 0.0035)^36 ]) / [ (1 + 0.0035)^36 – 1 ]

Simplifying the equation, we get:

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

p = p / [ (1 + 0.0035)^36 – 1 ] / [ 0.0035(1 + 0.0035)^36 ]

Q: What is the formula to calculate the monthly payment?

A: The formula to calculate the monthly payment is:

p = P [ i(1 + i)^t ] / [ (1 + i)^t – 1]

Where:

  • p = monthly payment
  • P = principal loan amount (the initial amount borrowed)
  • i = monthly interest rate (annual interest rate divided by 12)
  • t = number of payments (the number of months the loan is for)

Q: How do I calculate the monthly interest rate?

A: To calculate the monthly interest rate, you need to divide the annual interest rate by 12. For example, if the annual interest rate is 4.2%, the monthly interest rate would be:

i = r / 12 = 4.2 / 12 = 0.0035

Q: What is the total amount borrowed (P)?

A: The total amount borrowed (P) is the initial amount borrowed. It is the amount that you need to repay the bank.

Q: How do I calculate the total amount borrowed (P)?

A: To calculate the total amount borrowed (P), you need to use the formula:

P = p [ (1 + i)^t – 1 ] / [ i(1 + i)^t ]

Where:

  • p = monthly payment
  • i = monthly interest rate
  • t = number of payments

Q: What is the number of payments (t)?

A: The number of payments (t) is the number of months the loan is for. For example, if the loan is for 36 months, the number of payments would be 36.

Q: How do I calculate the number of payments (t)?

A: The number of payments (t) is given in the problem statement. For example, if the loan is for 36 months, the number of payments would be 36.

Q: What is the monthly payment (p)?

A: The monthly payment (p) is the amount that you need to pay each month to repay the loan.

Q: How do I calculate the monthly payment (p)?

A: To calculate the monthly payment (p), you need to use the formula:

p = P [ i(1 + i)^t ] / [ (1 + i)^t – 1]

Where:

  • P = total amount borrowed
  • i = monthly interest rate
  • t = number of payments

Q: What is the total amount repaid (T)?

A: The total amount repaid (T) is the total amount that you need to repay the bank. It is the sum of the monthly payments.

Q: How do I calculate the total amount repaid (T)?

A: To calculate the total amount repaid (T), you need to multiply the monthly payment (p) by the number of payments (t):

T = p * t

Where:

  • p = monthly payment
  • t = number of payments

Q: What is the interest paid (I)?

A: The interest paid (I) is the amount of interest that you need to pay the bank.

Q: How do I calculate the interest paid (I)?

A: To calculate the interest paid (I), you need to subtract the principal loan amount (P) from the total amount repaid (T):

I = T – P

Where:

  • T = total amount repaid
  • P = principal loan amount

Conclusion

Calculating the monthly payment is a complex process that involves several variables, including the principal loan amount, monthly interest rate, and number of payments. By using the formula and understanding the variables involved, you can calculate the monthly payment and total amount repaid.