Question

1. Ann buys a house for $4,000,000. She gets a mortgage for $3,200,000 and pays the rest. What is Ann’s Loan to Value (LTV) ratio at the time of purchase? Write the answer as a percent so for example 2.5% should be written as 2.5, not as 0.025.

2. Ann buys a house for $4,000,000. She gets a mortgage for $3,200,000 and pays the rest. How much home equity (HEQ) does Ann have?

3. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $3,200,000 at 4.38%. How much does Ann need to pay monthly?

4. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with annual payments for $3,200,000 at 4.38%. How much does Ann need to pay annually?

5. Ann obtains a fully amortizing 15 year Fixed Rate Mortgage with monthly payments for $3,200,000 at 4.38%. How much does Ann need to pay per month?

6. Ann is willing to spend $3,500 per month on her mortgage payment. If Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with monthly payments at 4.38%, how big of a mortgage can she get?

7. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $3,200,000 at 4.38%. What will be Ann’s mortgage balance after 20 years of payments (ie after 240 months)?

8. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $3,200,000 at 4.38%. What percent of Ann’s 20^th payment goes to interest?

9. Ann obtains a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $3,200,000 at 4.38%. What percent of Ann’s 20^th payment goes to principal?

10. Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $3,200,000.

Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.

Mortgage B has a 6% interest rate and requires Ann to pay zero fees upfront.

Assuming Ann makes payments for 30 years, what is Ann’s annualized IRR from mortgage A?

11. Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $3,200,000.

Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.

Mortgage B has a 6% interest rate and requires Ann to pay zero fees upfront.

Assuming Ann makes payments for 30 years, what is Ann’s annualized IRR from mortgage B?

12. Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $3,200,000.

Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.

Mortgage B has a 6% interest rate and requires Ann to pay zero fees upfront.

Assuming Ann makes payments for 30 years, which mortgage has the lowest cost of borrowing (ie lowest annualized IRR)? Type 1 for A, type 2 for B.

13. Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $3,200,000.

Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.

Mortgage B has a 6% interest rate and requires Ann to pay zero fees upfront.

Assuming Ann makes payments for 2 years before she sells the house and pays the bank the balance, what is Ann’s annualized IRR from mortgage A?

14. Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $3,200,000.

Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.

Mortgage B has a 6% interest rate and requires Ann to pay zero fees upfront.

Assuming Ann makes payments for 2 years before she sells the house and pays the bank the balance, what is Ann’s annualized IRR from mortgage B?

15. Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $3,200,000.

Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.

Mortgage B has a 6% interest rate and requires Ann to pay zero fees upfront.

Assuming Ann makes payments for 2 years before she sells the house and pays the bank the balance, which mortgage has the lowest cost of borrowing (ie lowest annualized IRR)? Type 1 for A, type 2 for B.

16. Ann obtains a 30-year Interest Only Fixed Rate Mortgage with monthly payments for $3,200,000 at 4.38%. What will Ann’s monthly payments be?

Answer 1

1. Loan To Value Ratio = Mortgage Amount / Asset Value = $3.2 million / $4 million

Loan To Value Ratio = 0.8 or 80%

2. Home Equity = Value of Asset - Mortgage Amount

Home Equity = $4 million - $3.2 million = $0.8 million

3.

Time to Maturity = 30 years or 360 monthly periods

Rate of Interest = 4.38% compounded monthly i.e 4.38/12 = 0.365% monthly

Mortgage Amount = $3200000

c = $15986.86

4.

Time to Maturity = 30 years

Rate of Interest = 4.38% compounded annually

Mortgage Amount = $3200000

c = $193698.17