Ann wants to buy an office building which costs $1,000,000. She obtains a 30 year fully...

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

Solutions

Expert Solution

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.

jeff jeffy answered 1 year ago

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