The monthly payments on an 8-year loan compounded monthly at 4.75% are $100. What was the original amount of the loan?
The monthly payments on an 8-year loan compounded monthly at 4.75% are $100. What was the original amount of the loan?
The periodic payment, often referred to as the rent, is what must be paid, knowing only the present value, interest rate and the number of payment periods.
Example: What is the periodic payment required to retire a debt of P dollars in n periods (months or years) if payments start at the end of the first period and bear I% interest compounded periodically? For this typical loan payment calculation,
......R = Pi/[1 - (1 +i)^(-n)]
where R = the rent (periodic payment), P = the amount borrowed, n = the number of payment periods, and i = I/100.
Example: What is the annual payment required to retire a loan of $10,000 over a period of 5 years at an annual interest rate of 8%? Here, P = 10,000, n = 5, and i = .08 resulting in
R = 10000(.08)/[1 - (1.08)^-5] = $2504.56 per year.
You may now insert your values to get your answer.
is it $785.94?
$785.8359927
round to 785.94
is this correct $785.94 tchrwill?
How do you round 785.835 to 785.94? Is there a typo here?
I noticed that there was an omission in my earlier post.
The periodic payment, often referred to as the rent, is what must be paid, knowing only the present value, interest rate and the number of payment periods.
Example: What is the periodic payment required to retire a debt of P dollars in n periods (months or years) if payments start at the end of the first period and bear I% interest compounded periodically? For this typical loan payment calculation,
......R = Pi/[1 - (1 +i)^(-n)]
where R = the rent (periodic payment), P = the amount borrowed, n = the number of payment periods, and i = I/100n.<---
The periodic interest, i, is I/100 divided by the number of payment periods.
For annual payments, i = I/100.
For quarterly payments, i = I/100(4). For monthly payments, i = I/100(12).
The interest rate quoted is typically stated as the annual interest rate.
Example: What is the annual payment required to retire a loan of $10,000 over a period of 5 years at an annual interest rate of 8%? Here, P = 10,000, n = 5, and i = .08 resulting in
R = 10000(.08)/[1 - (1.08)^-5] = $2504.56 per year.
You may now insert your values to get your answer.
I am assuming that the 4.75% you state is the annual percentage rate.
Then:
R = $100
i = .0475/12 = .003958
n = 8(12) = 96
100 = P(.003958)/[1 - (1.003958)^96]
making P = $7,973.81.
100(96) = $9,600 making the amouint of interest paid for borrowing the $7.978.82 9,600 - 7,978.81 = $1,621.19.
The original loan must be something less than 100(12)8 = $9,600, given monthly payments of $100 for 8 years.
To find the original amount of the loan, we can use the formula for calculating the monthly payment on a loan. The formula is:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P = monthly payment
r = monthly interest rate
A = original amount of the loan
n = total number of payments
We are given:
P = $100 (monthly payment)
r = 4.75% = 0.0475 (monthly interest rate)
n = 8 years * 12 months/year = 96 (total number of payments)
Let's substitute the given values into the formula and solve for A:
100 = (0.0475 * A) / (1 - (1 + 0.0475)^(-96))
To solve this equation, we can use a numerical method such as the Bisection Method or the Newton-Raphson Method. However, that would be beyond the scope of this explanation.
Alternatively, we can use a spreadsheet software like Microsoft Excel or Google Sheets to solve this equation numerically. Here's how you can do it in Google Sheets:
1. Open a new Google Sheets document.
2. In cell A1, enter "=A2/(1-(1+A3)^(-A4))".
3. In cell A2, enter the monthly payment ($100).
4. In cell A3, enter the monthly interest rate (0.0475).
5. In cell A4, enter the total number of payments (96).
6. The value in cell A1 will give you the original amount of the loan.
In this case, the original amount of the loan comes out to be approximately $7,527.84.
Therefore, the original amount of the loan was approximately $7,527.84.