In: Finance
Ann wants to buy an office building which costs $1,000,000. She obtains a 30 year fully amortizing fixed rate mortgage at 80% LTV, an annual interest rate of 4%, with monthly compounding and monthly payments. How much is Ann’s monthly payment?
A. $3,819.32 B. $2,666.67 C. $3,333.33 D. $4,774.15
Compute the value of loan, using the equation as shown below:
Loan value = Building cost*LTV ratio
= $1,000,000*80%
= $800,000
Hence, the value of the loan is $800,000.
Compute the monthly rate of interest, using the equation as shown below:
Monthly rate = Annual rate/ 12 months
= 4%/ 12 months
= 0.33333333333%
Hence, the monthly rate of interest is 0.33333333333%.
Compute the present value annuity factor (PVIFA), using the equation as shown below:
PVIFA = {1 – (1 + Rate)^-Number of periods}/ Rate
= {1 – (1 + 0.00333333333)^-360}/ 0.33333333333%
= 209.461240555
Hence, the present value annuity factor is 209.461240555.
Compute the monthly payment of the loan, using the equation as shown below:
Monthly payment = Loan amount/ PVIFA
= $800,000/ 209.461240555
= $3,819.32236188
Hence, the monthly payment of the loan is $3,819.32.