Question

Ann gets a fully amortizing 30-year fixed rate mortgage with monthly payments. The initial balance is $1,000,000. The interest rate is 3.50%, compounded monthly. What will be Ann’s loan balance after her 240th payment (if Ann makes exactly the required monthly payment for 20 years)?

Also, Using your answer from Q11, what fraction of the 241st payment will go to principal (in percent)?

Answer #1

Balance after 240^{th}
payment= **$454,104.01**

Fraction of 241^{st}
payment to principal= **70.50%**

Calculation as below:

Ann gets a fully amortizing 30-year fixed rate mortgage with
monthly payments. The initial balance is $1,000,000. The interest
rate is 3.50%, compounded monthly. What will be Ann’s loan balance
after her 240th payment (if Ann makes exactly the
required monthly payment for 20 years)?
Using your answer from abovr, what fraction of the 241st payment
will go to principal (in percent)?

Ann gets a fully amortizing 30-year fixed rate mortgage with
quarterly payments for $1,000,000. The interest rate is 4%,
compounded quarterly. She prepays the mortgage in 1 quarter (i.e.
she makes the 1st payment and immediately prepays the remaining
balance).
There is still an origination fee of 2 points, but now Ann
decides to keep the mortgage for the whole term, i.e. she no longer
plans to prepay it. What is Ann’s APR?

Ann is looking for a fully amortizing 30 year Fixed Rate
Mortgage with monthly payments for $4,500,000. 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.
(A) Assuming Ann makes payments for 30 years, what is Ann’s
annualized IRR from mortgage A?
(B) Assuming Ann makes payments for 30 years, what is Ann’s
annualized IRR from mortgage B?

1) Ann is looking for a fully amortizing 30 year Fixed Rate
Mortgage with monthly payments for $4,500,000.
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?
2)Ann is looking for a fully...

Ann is looking for a fully amortizing 30 year Fixed Rate
Mortgage with monthly payments for $4,500,000.
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?

Ann is looking for a fully amortizing 30 year Fixed Rate
Mortgage with monthly payments for $4,500,000.
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?

Ann is looking for a fully amortizing 30 year Fixed Rate
Mortgage with monthly payments for $4,500,000.
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 $135,000.
Mortgage A has a 5.25% 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...

14. Ann is looking for a fully amortizing 30 year Fixed Rate
Mortgage with monthly payments for $135,000.
Mortgage A has a 5.25% 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...

Ann obtains a fully amortizing 15 year Fixed Rate Mortgage with
monthly payments for $4,500,000 at 4.38%. How much does Ann need to
pay per month?

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