You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 35-year mortgage loan for 75 percent of the $3,250,000 purchase price. The monthly payment on this loan will be $15,800.

Requirement 1:
What is the APR on this loan? (Round your answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

Requirement 2:
What is the EAR on this loan? (Round your answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)

PV of loan = .75(3250000) = $2,437,500

paym = 15800
n = 12(35) =420
let the monthly rate be i
2437500 = 15800( 1 - (1+i)^-420)/i
154.2721519 i = 1 - (1+i)^-420

This is a very nasty equation to solve.
Back in the "good ol' days", we used a method called interpolation, and it took forever to do something like this.
Often there there tables and charts, but that n = 420 would have been beyond most of the n values in the chart, so that caused further problems.

I assume you have access to some software or calculator technology that will solve this for you.
Using Wolfram, I got i = .00594417
http://www.wolframalpha.com/input/?i=154.2721519+x+%3D+1+-+(1%2Bx)%5E-420
- notice I changed the i to x, it assumed i was a complex number.

check:
15800( 1-1.00594417)^-420)/.00594417
= 2,437,501.39
not bad, off by about $1 in 2 1/2 million!!

so if i = .00594417, then 12i = .07133
or 7.13% per annum compounded monthly

for b) I would simply find the annual rate j, so that

1+j = 1.00594417^12
j = .0737088...
So the effective annual rate is 7.37%

Why did the clown bring a calculator to the warehouse? Because he wanted to calculate the APR and EAR on his mortgage loan! Let's find out the answers.

Requirement 1:
To find the APR, we need to know the loan amount, monthly payment, and loan term. The loan term is 35 years, which means 420 months. The loan amount is 75% of $3,250,000, which is $2,437,500. And the monthly payment is $15,800.

Now let's do some calculations... *puts on nerd glasses*

APR = (Monthly Payment / Loan Amount) x (12 / Loan Term) x 100%

APR = ($15,800 / $2,437,500) x (12 / 420) x 100%

*types furiously on the calculator*

The APR on this loan is approximately 2.79%!

Requirement 2:
To find the EAR, we need the APR and the compounding frequency. Since we don't have the compounding frequency, let's assume it is monthly.

EAR = (1 + (APR / Number of Compounding Periods)) ^ Number of Compounding Periods - 1

EAR = (1 + (0.0279 / 12)) ^ 12 - 1

*calculates with exaggerated excitement*

The EAR on this loan is approximately 2.82%!

So there you have it - the clown's mortgage loan has an APR of 2.79% and an EAR of 2.82%. Now he can get back to juggling those financial responsibilities!

To find the APR (Annual Percentage Rate) and EAR (Effective Annual Rate) on the loan, we need to use some formulas.

The formula to calculate the APR is:

APR = ((Monthly Payment / Loan Amount) * 12) * 100

Substituting the given values:

Loan Amount = 0.75 * $3,250,000 = $2,437,500
Monthly Payment = $15,800

APR = (($15,800 / $2,437,500) * 12) * 100

Now let's calculate the APR:

APR = (0.00647692 * 12) * 100

APR ≈ 7.77%

Therefore, the APR on this loan is approximately 7.77%.

The formula to calculate the EAR is:

EAR = (1 + (APR / n))^n - 1

Here, n represents the number of compounding periods per year for the loan.

As the given information doesn't specify the compounding frequency, we'll assume it's compounded monthly (12 periods per year). So, n = 12.

Substituting the APR value we found into the EAR formula:

EAR = (1 + (0.0777 / 12))^12 - 1

Now let's calculate the EAR:

EAR = (1.006474063)^12 - 1

EAR ≈ 0.0934

Therefore, the EAR on this loan is approximately 9.34%.

To calculate the APR (Annual Percentage Rate) and EAR (Effective Annual Rate) on a loan, we need to know the loan amount, monthly payment, and loan term.

Given:
- Loan amount: $3,250,000
- Loan term: 35 years
- Monthly payment: $15,800

Requirement 1: Calculate the APR on this loan.

The APR represents the yearly interest rate charged on the loan. To calculate the APR, we can use the loan amount, monthly payment, and loan term.

1. First, let's calculate the total payment over the loan term. Multiply the monthly payment by the number of months in the loan term (35 years * 12 months/year):

Total Payment = Monthly payment * Number of months
Total Payment = $15,800 * (35 * 12)
Total Payment = $15,800 * 420 = $6,636,000

2. Next, subtract the loan amount from the total payment to calculate the interest paid:

Interest Paid = Total Payment - Loan Amount
Interest Paid = $6,636,000 - $3,250,000
Interest Paid = $3,386,000

3. Now, calculate the APR by dividing the interest paid by the loan amount and multiplying by 100 to convert it to a percentage:

APR = (Interest Paid / Loan Amount) * 100
APR = ($3,386,000 / $3,250,000) * 100
APR = 104.25

So, the APR on this loan is 104.25%.

Requirement 2: Calculate the EAR on this loan.

The EAR represents the true annual interest rate when compounding is considered. To calculate the EAR, we need to know the APR and the compounding frequency.

Assuming monthly compounding, the formula to calculate the EAR is:

EAR = (1 + (APR / Number of compounding periods))^Number of compounding periods - 1

1. First, convert the APR to a decimal by dividing it by 100:

APR_decimal = 104.25 / 100
APR_decimal = 1.0425

2. Next, substitute the values into the formula:

EAR = (1 + (APR_decimal / 12))^12 - 1
EAR = (1 + (1.0425 / 12))^12 - 1

3. Calculate the EAR:

EAR = (1 + 0.086875)^12 - 1
EAR = (1.086875)^12 - 1
EAR = 1.973044104 - 1
EAR = 0.973044104

4. Convert the EAR to a percentage by multiplying it by 100:

EAR_percentage = EAR * 100
EAR_percentage = 0.973044104 * 100
EAR_percentage = 97.30

So, the EAR on this loan is 97.30%.