Ch. 18 Self Assessment

Consider an adjustable-rate mortgage (ARM) loan for $143,000. The interest rate is indexed to the 1-year T-bill yield. The loan has a margin of 2%, a one-year teaser rate of 1%, an annual rate cap of 2% and a lifetime rate cap of 5%. The loan requires monthly payments for 15 years. The lender charges 1 point at origination. Assume that T-Bill yields are as follows: At origination (months 1-12) 3.5% At end of first year (months 13-24) 5.3% What is the payment amount during months 13 through 24?

$1,237 CLR TVM 143,000 PV, 15 x 12 = 180 N, (3.5 + 2 -1)/12 = .375 I/Y, CPT PMT The payments for the first 12 months are 1,093.94 Now, do a prepayment and then a refinancing calculation: After 1 year, 180 - 12 = 168 payments are left. Change N: 168 N, CPT PV PV = 136,167.95 Change the interest rate to the new contract rate: 5.3 + 2 = 7.3%. However, the annual cap does not allow the year two rate to be more than 2% over the first year contract rate (which is 4.5%). Therefore, the contract rate for year 2 is 6.5%. 6.5/12 = .54167 I/Y, CPT PMT. The payments during the 2nd year of the loan are 1,236.54

A lender makes a $90,000 mortgage at 9% interest with monthly payments for 25 years. How much principal will be repaid during the fourth year of the loan?

$1,314 CLR TVM 90,000 PV, 9/12 = .75 I/Y, 25 x 12 = 300 N, CPT PMT PMT = -755.28 2nd AMORT, P1 = 37, P2 = 48, PRN = 1,313.97

You are buying a $162,000 house with a 20% down payment and a fixed-rate mortgage for the remainder at 8.75% for 30 years with monthly payments. What is the balance or amount outstanding on the loan at the end of the fourth year?

$125,333.08 First enter all the 4 variables for this loan into the TVM keys: CLR TVM 162,000 x .8 = 129,600 PV, 8.75/12 = .72917 I/Y, 30 x 12 = 360 PV, CPT PMT PMT = -1,019.56 Now go into the amortization function: 2nd, AMORT, P1 = 48 ENTER, P2= 48 ENTER, BAL = 125,333.08 (Note: P1 can be set to any number between 1 and 48)

Assume you have a mortgage that has 276 payments and an amount outstanding of $382,642.76 left. What is the current payment if the original interest rate is 6.25% and what is the new payment, if you can refinance at an interest rate of 5%.

$2,616.80 and $2,335.67 CLR TVM 276 N, 382,642.76 PV, 6.25/12 = .52083 I/Y, CPT PMT The current payment it $2,616.80. Change the rate to 5/12 = .4167 I/Y, CPT PMT. The new payments with the lower interest rate would be $2,335.67.

You are buying a $162,000 house with a 20% down payment and a fixed-rate mortgage for the remainder at 8.75% for 30 years with monthly payments. How much total interest is due over the full term of the loan?

$237,442.94 First enter all the 4 variables for this loan into the TVM keys: CLR TVM 162,000 x .8 = 129,600 PV, 8.75/12 = .72917 I/Y, 30 x 12 = 360 PV, CPT PMT PMT = -1,019.56 Now go into the amortization function: 2nd, AMORT, P1 = 1 ENTER, P2= 360 ENTER, INT = -237,442.94

A buyer can afford no more than $500 per month in payments. The most favorable loan available in the market is a 30 year, monthly payment loan at 10% APR. What is the maximum affordable house with a 10% down payment?

$63,306 CLR TVM 500 PMT, 30 x 12 = 360 N, 10/12 = .83333 I/Y, CPT PV PV = -56,975.41 The bank will lend the buyer $56,975.41. If the down payment is 10%, then the loan to value ratio is 90%, or .9. This means loan divided by value = .9. Solve this formula for the "Value". L/V = .9, V = L/.9 56,975.41/.9 = 63,306

Consider an adjustable rate mortgage of $90,000 with a maturity of 30 years and monthly payments. At the end of each year, the interest rate is adjusted to become two percentage points above the index. There is an annual cap of 300 basis points (3%), and a lifetime cap of 500 basis points (5%). In the first year the contract rate is 7%, with no teaser. In year two, the index rate is 9%. What monthly payment is called for in year two?

$786 CLR TVM 90,000 PV, 30 x 12 = 360 N, 7/12= .5833 I/Y, CPT PMT The payments in the first year are $598.77. For year 2: First do a prepayment and then a refinancing calculation. Change N to N remaining: 360 - 12 = 348 N, CPT PV PV = 89,085.77 Change I/Y to the new contract rate 10/12 = .8333 I/Y, CPT PMT The payments in the 2nd year are $786.16. Note that in year two, the rate is calculated as 9% + 2% = 11%. However, because of the annual cap of 3%, the rate can only increase to 10%.

Consider a two-step mortgage for $150,000, 30 years, monthly payments, an initial interest rate of 5%, a cap of 5%, and a single rate adjustment at the end of year 7. What is the payment amount during the first 7 years of this loan?

$805 CLR TVM 150,000 PV, 30 x 12 = 360 N, 5/12 = .4167 I/Y, CPT PMT The payment amount is $805.23.

You are buying a $162,000 house with a 20% down payment and a fixed-rate mortgage for the remainder at 8.75% for 30 years with monthly payments. How much interest is paid in the 49th payment?

$913.89 CLR TVM 162,000 x .8 = 129,600 PV, 8.75%/12 = .7292I/Y, 30 x 12 = 360 N, CPT PMT PMT = -1,019.56 2nd AMORT P1 = 49 ENTER, P2 = 49 ENTER INT = -913.89

Consider a two-step mortgage for $150,000, 30 years, monthly payments, an initial interest rate of 5%, a cap of 5%, and a single rate adjustment at the end of year 7. If the index rate at the end of year 7 is 5% and the margin is 2%, what is the payment amount during the last 23 years of this loan?

$963 CLR TVM 150,000 PV, 30 x 12 = 360 N, 5/12 = .4167 I/Y, CPT PMT PMT = -$805.23 Now, do the prepayment and then a refinancing calculation. First, change the N to remaining after 7 years: 23 x 12 = 276 N, and solve for PV. CPT PV PV = -131,917.52 Now, do a refinancing calculation: change the interest rate to the new rate at year 7: 7%/12 = .5833 I/Y, CPT PMT The new payments starting in year 7 are 962.89.

Consider an adjustable rate mortgage of $90,000 with a maturity of 30 years and monthly payments. At the end of each year, the interest rate is adjusted to become two percentage points above the index. There is an annual cap of 300 basis points (3%), and a lifetime cap of 500 basis points (5%). In the first year the contract rate is 7%, with no teaser. In year two, the index rate is 9%. What is the contract rate in year two?

10% 9% + 2% = 11%. However, since the annual cap is 3% and the year one contract rate is 7%, the year two contract rate is 10%.

A borrower is offered a mortgage loan for $100,000 with an interest rate of 10% and a 30-year amortization period with monthly payments. The origination fee is 1% of the loan and the lender charges two discount points. What is the effective interest rate?

10.37% APR First, calculate the payment for this loan. CLR TVM 100,000 PV, 10/12 = .8333 I/Y, 30 x 12 = 360 N, CPT PMT PMT = -877.57 Now change the PV to the net amount of the loan. The fees are (100,000 x .01) + (100,000 x .02) = 3,000 100,000 - 3,000 = 97,000 PV CPT I/Y I/Y = .8638 .8638 x 12 = 10.37 APR

If the initial contract rate on an ARM is 6%, the second year contract rate is 9%, the margin is 2%, the life of the loan cap is 5%, and the annual cap is 3%, what is the contract rate for year three if the index is 9%?

11% 9% + 2% = 11%

The index for year one in an AMR loan is 6%, the margin is 2%, the lifetime cap is 6%, the annual cap is 2%, and the first-year-only teaser is 1%. The maximum interest rate allowable during the life of the mortgage is

13%. First year contract rate: 6% + 2% - 1% = 7% Maximum rate for the life of the loan: 7% + 6% = 13%

Assume you get a quote from a bank for a 30-year monthly payment fixed rate mortgage for $425,000 at 6.25% APR. What is the mortgage payment on this loan?

2,616.80 CLR TVM 30 x 12 = 360 N, 425,000 PV, 6.25/12 = .52083 I/Y, CPT PMT The mortgage payment is $2,616.80

Assume you get a quote from a bank for a 30-year monthly payment fixed rate mortgage for $425,000 at 6.25% APR. How much in interest would you have to pay in year 2?

26,101.11 CLR TVM 30 x 12 = 360 N, 425,000 PV, 6.25/12 = .52083 I/Y, CPT PMT PMT = -2,616.80 Now, go to the AMORT function by hitting 2nd AMORT. P1=13 ENTER, P2 = 24 ENTER, scroll down until you see INT. INT for year 2= -26,101.11

How many discount points are necessary to raise the yield of a 12% APR loan with 360 monthly payments of $514.30 to 12.42%? (Hint: find the present value of the annuity under each interest rate then examine the difference!)

3 First find the loan amount (PV) for the loan using the original input variables: CLR TVM 12/12=1 I/Y, 360 N, 514.30 PMT, CPT PV PV = -49,999.39 Next, find the loan amount if the rate (yield) is 12.42% APR: CLR TVM 12.42/12=1.035 I/Y, 360 N, 514.30 PMT, CPT PV PV = -48,470.68 The difference between the two loan amounts is 49,999.38 - 48,470.68 = 1,528.71 Now, find the points that equate to $1,528.71 for a $49,999.39 mortgage. Or in other words, what percentage is $1,528.71 of $49,999.39? 1,528.71/49,999.39 = .0306 or 3%

Assume you get a quote from a bank for a 30-year monthly payment fixed rate mortgage for $425,000 at 6.25% APR. How much would you owe after 7 years, if you decide to sell the house then?

382,642.76 CLR TVM 30 x 12 = 360 N, 425,000 PV, 6.25/12 = .52083 I/Y, CPT PMT PMT = -2,616.80 Now, go to the AMORT function by hitting 2nd AMORT. P1= 84 ENTER, P2 = 84 ENTER, scroll until you see BAL. The BAL at the end of year 7 is 382,642.76.

Assume that a bank quotes you a 30-year monthly payment fixed rate mortgage for $425,000 at 6% APR and charges you two points. If you decided to take on that and then prepaid the loan after 7 years (84 months), what would be your effective interest rate be?

6.37 APR Note: the fees are $425,000 x .02 = $8,500 Step 1: Prepayment CLR TVM 30x 12 = 360 N, 425,000 PV, 6/12 = .5 I/Y CPT PMT PMT = -2,548.09 Change N to N remaining after 7 years: 276 N, CPT PV 380,967.39 (Note: you can also use the AMORT function and set P1 and P2 to 84, then find the BAL) Step 2: TVM calculation where you use all 5 TVM keys. You have to solve for the I/Y! 380,967.39 FV (this is the answer from the prepayment calculation above) 84 N (this is the time of prepayment) 2,548.09 PMT (this is the monthly payment for this loan) -416,500 PV (this is the original loan amount of $425,000 less the $8,500 in fees) CPT I/Y I/Y = .5309285 .5309285 x 12 = 6.3711 APR This is the effective rate considering points and prepayment.

The index for year one in an AMR loan is 6%, the margin is 2%, the lifetime cap is 6%, the annual cap is 2%, and the first-year-only teaser is 1%. What is the first year contract rate?

7% 6% + 2% - 1% = 7%

Which of the following is true for a "negative amortization" loan?

An "option" adjustable rate mortgage is a negative amortization loan

A refinancing decision is a very simple type of decision. A borrower should refinance his or her mortgage loan as soon as interest rates drop.

FALSE

Bob is considering fixed-rate loans from two different lenders who are willing to finance the purchase of a home. The loan amount is $90,000. Lender A is offering a 30-year, monthly payment loan at 7% interest with 2.5 points. Lender B is offering a 30-year, monthly payment loan at 7.5% interest with no points. Which of the following bits of advice would be best for Bob assuming he does not plan to prepay either loan? (Hint: find the effective interest rate on each loan and compare.)

Loan A is better. To compare apples to apples, you have to convert the interest rate for loan A into an effective interest rate. Loan A: CLR TVM 90,000 PV, 30 x 12 = 360 N, 7/12 = .5833 I/Y, CPT PMT PMT = -598.77 The fees on this loan are: 90,000 x .025 = 2,250 Change the present value to the loan amount less the fees: 90,000 - 2,250 = 87,750. 87,750 PV, CPT I/Y I/Y = .6044 .6044 x 12 = 7.2527 APR Loan A has a lower effective rate (7.2527 APR) than loan B (7.5% APR).

As an alternative to the fixed-rate mortgage, borrowers can often obtain an adjustable rate mortgage which has an initial interest rate below that of fixed-rate loans. The reason why lenders accept a lower initial rate is because the borrower bears some of the risk should the rate change in the future.

TRUE

Financial models should always have an assumption section so that it is easier to make the model "dynamic".

TRUE

The sooner a borrower prepays a loan with points, the higher the effective interest rate will be.

TRUE

Which of the following mortgages has mortgage payments reestablished once during the life of the loan?

Two-step

To reduce the risk to the borrower, adjustable rate mortgages typically have

an interest rate cap.

Two-step mortgages are attractive to

borrowers who don't expect to own the property for the entire length of the loan.

When a mortgage loan with level periodic payments has been completely repaid by the maturity date, it is said to be

fully amortized.

Loans made for a stated term on which interest payments are due periodically but whose principal is not repaid until the end of the term are called

interest only loans.

Which of the following statements does not apply to employing the amortization method of repaying a mortgage loan? The amount of the

payment applied to principal repayment decreases each period.

Amortization is the

process of gradually retiring a debt by periodic payments.

What must be true for a fixed rate mortgage that has a balloon payment at the end of the loan term? (See student activity for the chapter)

the term of the mortgage is shorter than the amortization period