Question

No execel please! I am trying to learn the math for the exam! Thank you!!

Shanna wants to buy a house costing $325,000 and has obtained a loan from TD Bank. A minimum down payment of 15% would be required and the bank will provide the difference. Her grandparent have told her that they will cover her down payment.

a. TD Bank has quoted her mortgage interest rate is 4.5%; this rate would be compounded semiannually, while her payments would be made monthly. What is the effective monthly interest rate (EMR) that she would pay?

b. Calculate her monthly mortgage payment, assuming 15% down payment from her grandparents and a mortgage maturity of 25 years.

c. Given (b) above, how much of her payment in the 2nd month will go toward repayment of principal and how much is interest payment?

d. Assuming that five years later, interest rates drop to 3.2% and Shanna decides to refinance the mortgage. How much would she have paid in interest and how much of the original loan have you paid over the five years?

e. Suppose she decides to refinance your mortgage to take advantage of the reduced interest rate. How would her monthly payments change if she could refinance her mortgage at 3.2% (with a 20-year term loan)?

f. Suppose she kept her monthly payments at the original amount found in (b) above at 4.5%, but refinanced the at 3.2%, how long would it take her to pay off the mortgage?

Answer 1

a). Calculation of Effective monthly interest (EMR) rate :

Formula for Effective monthly interest (EMR) rate = [ 1+ (Stated interest rate/n]n -1

where;

n= number of times the interest is compounded per annum.

Effective monthly interest (EMR) rate =(1+0.045/12)^12-1 = 0.0459 or 4.59%

Effective monthly interest rate she would pay 4.59% per annum monthly compounding.

Note: Since question asked about monthly effective interest rate, it is compounded at monthly i.e., number of times compounding is 12 p.a

b). Calculation of monthly mortgage payment, when 15% down payment has been paid by her grandparents and mortgage periods are 25 years:

Cost of house $325,000.

Down payment 15%= $325,000 x 15% = $48,750

Therefore, mortgage loan would be $276,250 repayment period of 25 years or 300 EMI.

Calculation of equated monthly repayment( EMI) over next 25 years or 300 months:

To calculate EMI formula is: =P x R x (1+R)^N/((1+R)^N-1)

Where:

P= Principal loan

R= Rate of interest = 4.5%p.a. or 4.5%/12= 0.00375% per month

N= Repayment periods

EMI= $276,250 x 0.00375 x (1.00375)^300/(1.00375)^300-1

EMI or monthly mortgage payment = $1,535.48722

c). Calculation of repayment of principal and interest payment for 2nd month as per of her EMI schedule as follows:

	REPAYMENT SCHEDULE
Installment	Outstanding at the beginning	Principal repayment	Interest	Amount paid	Outstanding at the end
1	276250.0000	499.5497	1035.9375	1535.4872	275750.4503
2	275750.4503	501.4230	1034.0642	1535.4872	275249.0272

As per above repayment schedule the 2nd months' repayment of principal and payment of interest would be $501.4230 and $1,034.0642 respectively.

d). After 5 years or after 60 EMI the amount of interest payment and amount of repayment of original loan has been paid by Shanna as follows:

As per repayment schedule after 5 years or after 60 EMI payment Shanna has been repaid the original loan/principal and interest payment would be $33,542.5418 and $58,586.6914.

Note: Prepare repayment schedule for 300 months with the above given information and cumulative amount of principal repayment for 60 months would $33,542.5418 be and cumulative amount of interest payment would be $58,586.6914.

e). Suppose she decides to refinance your mortgage to take advantage of the reduced interest rate. How would her monthly payments change if she could refinance her mortgage at 3.2% (with a 20-year term loan)?

After 5 year cumulative repayment of original principal would be $33,542.5418.

Therefore, balance of original loan after 5 years would be $276,250 less repayment $33,542.5418 = $242,707.4582

Calculation of Equated monthly repayment( EMI) over next 20 years or 240 months:

To calculate EMI formula is: = P x R x (1+R)^N/((1+R)^N-1)

Where:

P= Principal loan

R= Rate of interest = 3.2%p.a. or 3.2%/12= 0.002667% per month

N= Repayment periods

EMI= $242,707.4582 x 0.002667 x (1.002667)^240/(1.002667)^240-1

EMI or monthly mortgage payment = $1,370.4788

If mortgage rate drop from 4.5% P.a. to 3.2% P.a after 5 years from now then, EMI of Shanna would be reduced from $1,535.48722 to $1,370.4788 which would be payable by her for remaining 20 years or 240 EMI.

f). Suppose she kept her monthly payments at the original amount found in (b) above at 4.5%, but refinanced the at 3.2%, how long would it take her to pay off the mortgage?

If Shanna should repay the original EMI of $1,535.4872 (as per b above) but she availed 3.2% P.a. revised interest rate then her loan fully pay-off as follows:

Prepare a repayment schedule with EMI of $1,535.4872 and monthly interest rate of 0.002667% or 3.2% P.a. the loan balance of $242,707.4582 would be pay-off approximately after paying 205.5 EMI starting from 61 month.