Respuesta :
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%
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%
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:
[tex]\text{PV}=\text{PMT}\times\dfrac{1-\left ( \dfrac1{(1+r)^n} \right )}{r}[/tex]
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
[tex]\begin{aligned} \text{2,320,000}&=\text{14,900}\times\dfrac{1-\left ( \dfrac1{(1+r)^{360}} \right )}{r}\\r&=0.560\%.\end{aligned}[/tex]
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:
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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.
