Question

You have just purchased a new warehouse. to finance the purchase, you’ve arranged for a 30-year mortgage loan for 80 percent of the $2,900,000 purchase price. the monthly payment on this loan will be $14,900. requirement 1: what is the apr on this loan?

Answer 1

The annual percentage rate on the loan is 6.72%

Further Explanation:

Annual Percentage Rate: It measures the rate of return earned on the investment or Rate charged on the loan.  

Calculate the Annual percentage rate:  

To calculate the APR we will calculate the present value of the annuity stream:

$\text{PV}=\text{PMT}\times\dfrac{1-\left ( \dfrac1{(1+r)^n} \right )}{r}$

   

Where,

PV = the present value of an annuity stream

PMT = the annual future payment

r = the interest rate or the discount rate

n = the number of periods  

$\begin{aligned} \text{2,320,000}&=\text{14,900}\times\dfrac{1-\left ( \dfrac1{(1+r)^{360}} \right )}{r}\\r&=0.560\%.\end{aligned}$    

And,  

Annual percentage rate   = 0.560 × 12

                                              = 6.72%

                                                   

Therefore, the annual percentage rate on the loan is 6.72%.

Working Notes:

Amount Borrowed = $2,900,000 × 0.80

                              =$2,320,000

Learn more:

1. Learn more about the lifetime cost of the loan along with interest

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2. Learn more about the interest on credit card

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3. Learn more about compound interest

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Answer details:

Grade: High School

Subject: Financial Management

Chapter: Time value of money

Keywords: You have just purchased a new warehouse. to finance the purchase, you’ve arranged for a 30-year mortgage loan for 80 percent of the $2,900,000 purchase price,  the monthly payment on this loan will be $14,900. Requirement, what is the apr on this loan.

Answer 2

We are asked to find the APR on this load.
Given:
Purchased price: $2,900,000
Monthly payment: 14,900
Amount borrowed: 0.80($2,900,000) = $2,320,000

Using the PVA equation:
PVA = $2,320,000 = $14,900 [{1-1/(1+r)]^360}/r]
r = 0.560%

APR is the monthly interest rate times the number in months of the year. 
APR = 12(.560) = 6.72%