25.Largent Supplies Corp. has borrowed to invest in a project. The loan calls for a payment of $17,384 every month for three years. The lender quoted Largent a rate of 8.40 percent with monthly compounding. At what rate would you discount the payments to find amount borrowed by Largent?

8.73%

none of the above

To find the amount borrowed by Largent, we need to discount the monthly payments of $17,384 over a period of three years, using the given interest rate of 8.40% with monthly compounding.

First, we need to calculate the number of compounding periods over the three-year period. Since the loan calls for monthly payments, there will be a total of 12 compounding periods per year, and therefore, 12 x 3 = 36 compounding periods over three years.

Next, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the loan (the total amount repaid)
P = the principal amount (amount borrowed)
r = the interest rate (in decimal form)
n = the number of compounding periods per year
t = the number of years

We want to find the principal amount, P, so we rearrange the formula:

P = A / (1 + r/n)^(nt)

Plugging in the given values:
A = $17,384 (monthly payment)
r = 8.40% = 0.084 (in decimal form)
n = 12 (compounding periods per year)
t = 3 (number of years)

P = $17,384 / (1 + 0.084/12)^(12*3)

Calculating the expression inside the parentheses:
(1 + 0.084/12)^(12*3) ≈ 1.2819

Now we can substitute this value into the formula:

P = $17,384 / 1.2819

P ≈ $13,559.91

Therefore, the amount borrowed by Largent is approximately $13,559.91.

To find the amount borrowed by Largent, we need to discount the payments they make each month. The formula to calculate the present value of an annuity is:

PV = PMT * [(1 - (1 + r)^(-n)) / r]

Where:
PV = Present Value (amount borrowed)
PMT = Payment per period ($17,384)
r = Interest rate per period (what we need to find)
n = Number of periods (in this case, 36 months)

In this case, we need to solve for r. Rearranging the formula, we can isolate r:

r = [(1 - (PV / PMT)) ^ -1/n] - 1

In this equation, PV is divided by PMT because we're trying to find r, the interest rate.

However, to find the interest rate using this equation, we would need to know the present value of the loan. Without that information, we cannot determine the exact interest rate at which the payments should be discounted.

If you have the present value of the loan (or any other information that can help determine the present value), you can substitute the values into the equation and calculate the interest rate.

For example, if you know the present value is $100,000, you can solve for r:

r = [(1 - (100,000 / 17,384)) ^ -1/36] - 1

Calculating this equation will give you the interest rate at which you should discount the payments to find the amount borrowed by Largent.