3. You have purchased a new warehouse for $4 million. To finance the purchase, you have arranged for a 30-year mortgage for 75 percent of the purchase price. The monthly payment on the loan will be $30,000 with zero balance after the final payment.
a. What is the APR on the loan?
b. What is the EAR?
Information provided:
Mortgage= present value= 0.75*$4,000,000 = $3,000,000
Time= 30 years*12 = 360 months
Monthly payment = $30,000
a. The yield to maturity is calculated by entering the below in a financial calculator:
PV= -3,000,000
PMT= 30,000
N= 360
Press the CPT key and I/Y to compute the yield to maturity.
The value obtained is 0.9689.
Therefore, the APR is 0.9689%*12 = 11.6271% 11.63%.
b.Effective annual rate is calculated using the below formula:
EAR= (1+r/n)^n-1
Where r is the interest rate and n is the number of compounding periods in one year.
EAR= (1+0.1163/ 12)^12 - 1
= 1.122704
= 0.122704*100
= 12.27%.
In case of any query, kindly comment on the solution.
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