You have just purchased a new warehouse. To finance the purchase, you’ve arrange
ID: 2771657 • Letter: Y
Question
You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 36-year mortgage loan for 70 percent of the $3,260,000 purchase price. The monthly payment on this loan will be $15,900.
What is the APR on this loan?
What is the EAR on this loan?
You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 36-year mortgage loan for 70 percent of the $3,260,000 purchase price. The monthly payment on this loan will be $15,900.
What is the APR on this loan?
What is the EAR on this loan?
Explanation / Answer
Loan Amount = 70% of $3,260,000 = $2282000
Monthly payment (P) = $15900
Time (n) = 36 years = 432 months
Let, Monthly interest rate = R
Thus,
As per the formula of present value of annuity
Loan Amount = P*(1-1/(1+R)^n)/R
Loan Amount =15900*(1-1/(1+R)^432)/R
At R = .6%
PV of loan payment = $2450051
At R =.7%
PV of loan payment = $2159853
Thus, as per the method of interpolation
R = .6% + ((PV of loan at .6% - Loan amount) / (PV of loan at .6% - PV of loan at .7%))*(.7% - .6%)
R = .6% + ((2450051 – 2282000) / (2450051 –2159853)) *(.7% - .6%)
R = .657% approx.
APR (Nominal) = Monthly rate of interest*12 = .657*12 = 7.884%
EAR = (1+R) ^12 – 1 = (1.00657)^12 – 1 = 8.175%
APR (effective) will be same as EAR.
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