## Quiz 4 :

Fixed Interest Rate Mortgage Loans

Answer:

The Federal Truth-in-Lending Act (FTL) is a legislation which makes it mandatory for lenders to make uniform disclosure of financial information contained in loan agreements. This disclosure will help borrowers to make comparison of cost of different loan agreements. The FTL legislation requires that three days after a mortgage application is made by the borrower, the lender must make the disclosures.

A very important disclosure is about the Annual Percentage Rate (APR) being charged on the loan. The FTL guidelines require accurate disclosure of the APR. Rounding of the APR to the nearest one-quarter of a percent is allowed as long as it falls within the nearest one-eighth of a percent of the APR computed as per the method prescribed in the FTL.

The legislation also requires disclosure of change in market interest rates and its effect on APR from the time of application until making of the loan. The lender must make prior additional disclosures to the borrower before making such loan. Thus, borrower will get to know the actual interest to be charged on loan before taking the loan.

Answer:

Introduction:

Constant payment mortgage loan (CPM) is the payment pattern used in the real estate for financing residential properties. Constant payment mortgage is used primarily for financing apartment, complexes, and shopping centres.

a.

Computation of payments at the beginning of year:

The initial monthly payment will be kept at $498.57. The payments at the beginning of year 2, 3, 4, and 5 will be computed with the help of excel.

Following are the formulas entered in excel to compute the payments at the beginning of the period.

Following is the results of the above entered formulas in excel:

The monthly payments for year 1, 2, 3, 4, and 5 will be $1,083.33, $1,080.83, $1,078.33, $1,075.83 and $1,073.33 respectively.

b.

Computation of payment under GPM (graduated payment mortgage):

The payments for the different years under GPM will be computed with the help of excel.

Following are the formulas entered in excel to compute the loan balances:

Following is the results of the above entered formulas in excel:

Therefore the balance at the end of year three will be

c.

The interest rate on the loan is 9 percent. The loan originated with four discount points.

Hence, the effective yield will be

Answer:

(a) Determine the monthly payment:

Monthly payment is the amount to be paid for the loan repayment. As a text book notation, financial calculator should be used to calculate the monthly payment (PMT).

It is given that the borrower obtains a loan of $100,000 at 6% interest for 20 years. These annual details should be converted into monthly details by dividing the interest with 12 and the number of periods will be 240 (20 years × 12).

The following inputs should be given to the financial calculator to derive the monthly payment:

With the help of the financial calculator or spreadsheet, the monthly payment (PMT) can be determined as

.

(b) Determine the total of payments for the entire 20-year period and the interest portion:

It is calculated that the monthly payment will be $716.43. Number of periods is 240.

Calculate the total of payments as follows:

Hence, the total amount payable for 240 periods will be

.

Among this total payment, $100,000 will be the principal portion and the balance of $171,943.45 ($271,943.35 - $100,000) would be the interest payment.

(c) Determine the amount of outstanding loan if the loan is repaid at the end of 8 years:

It is given that the borrower obtains a loan of $100,000 at 6% interest. If the loan is repaid at the end of 8 years, calculate the present value of future payments for the remaining 12 years of out 20 years' time period of the loan.

Total number of periods will be 144 (12 years × 12). The monthly interest rate will remain at 0.50%.

The following inputs should be given to the financial calculator to derive the monthly payment:

Solve for amount:

With the help of the financial calculator, the present value can be determined as

The amount of interest paid is the difference between the principal portion and the sum of total payments made and the mortgage balance at the end of 8 years calculated as below:

Hence, the total interest collected will be

.

Calculate the principal paid as follows:

Therefore, the principal payment is

(d) (1) Determine the new loan maturity balance assuming that loan payments are not made:

First determine the balance of loan after deducting $5,000 payment. In this regard, determine the present value of loan at the end of 8 th year (remaining years 12 years). The rate of interest per month is 0.5% and the number of period will be 144 (12 × 12 years).

Provide the following inputs to determine the present value of the remaining loan at the end of year 8:

Solve for payment:

With the help of the financial calculator, the present value can be determined as

Now determine the outstanding balance after the payment of $5,000 as below:

Now, determine the number of periods for the new loan maturity with the interest rate of 0.5%, monthly payment as $716.43 and the present value of loan as $68,416.22. Input these details in the financial calculator to determine the number of periods as below:

Solve for maturity:

Using the financial calculator, the number of periods can be determined as

.

(2) Determine the new monthly payment assuming loan maturity will not be reduced:

If the loan maturity will not be reduced, the number of periods will remain at 144 periods (12 × 12 years), rate of interest per month is 0.5%, and the present value of loan is $68,416.22.

Input these details in the financial calculator to determine the monthly payment as below:

Solve for payment:

Using the financial calculator, the monthly payment can be determined as

.

Note: Rounding off used therefore, answers calculate by others might be different in fractions.