Question

0. Read examples 6 and 7 in the text

1. Write an instruction describing amortization tables in your words. Tell what information in the columns, how the information in the three main column is calculated, and why it is useful, Do not use specific numbers, mathematical symbols, or excel functions, or cell references, Be sure to explain the calculations for the three columns.

2. Find the median home price for a city where you would like to live. Tell how you found it. Give a website if appropriate. Then, tell what the city is, why you would like to live there, and what the median home price is in two to five complete English sentences.

3. You will probably have to make a down payment of 20% for your dream house. Since this is a hypothetical situation, assume your instructor will give you the money for the down payment if you don't have it, so your loan will be for 80% of the median price. State this amount clearly and explain how you got it.

9:38 PM Mon May 20 Example 6. Amortization Schedule Continuing Example 5: Mortgage interest is tax deductible, so it is important to know how much of a year's mortgage payments repre- sents interest. How much interest will Marc and Mira pay in the first year of their mortgage? $60.39 60 89,939.61 89,817.62 89,756.01 89,693.99 62.43 89,568.71 89,505.44 597.12 596.70 89.44175 89,377 64 10 89,313.10 89,248.13 12 95.42 $7,172.81 Solution Let us calculate how much of each month's payment is interest and how much goes to reducing the outstanding principal. At the end of the first month, Marc and Mira must pay 1 month's interest on $90,000, which is $go,ooo x 0.08- $600 boO Less than a minute 55 pages left Example 7. Mortgage Refinancing Continuing Example 5: Ten years into Marc and Mira's mortgage, interest rates have fallen considerably, and they are considering refi- nancing the total they still owe with a new 20-year mortgage at anoth er bank at a rate of 5.5% . The bank where they have their current mortgage charges a prepayment penalty of 2% of the outstanding principal. What will their new monthly payments be if they go ahead with the refinance? Solution Using the formula in the "Before we go on" discussion above, we calculate the outstanding principal after 1o years to be (n -k) Outstanding principal PMT11 660391-+ 0.08/12)-(60-120) o.08/12 $78,952.46 The 2% prepayment penalty boosts the amount they owe to 78,952.46 x 1.02 - $80,531.51. Refinancing this amount at 5.5% interest for 20 years therefore re- sults in monthly payments of o.055/12 - 80,531.51 31- (1+ o.055/12) $553.97, so their monthly payments would decrease by 660.39 - 553.97 -$106.42. Using Technology Less than a minute 53 pages left 9:38 PM Mon May 20 The remainder of their first monthly payment, S660.39- 600- $60.39, goes to reducing the principal. Thus, in the second month the outstanding principal is $90,000 - 60.39 $89,939.61, and part of their second monthly pay- ment will be for the interest on this amount, which is $89.939.61 x 910 $599.60 The remaining $660.39 - $599.60 $60.79 goes to further reduce the principal. If we continue this calculation for the 12 months of the first year, we get the beginning of the mortgage's amortization schedule, shown in the margin. As we can see from the totals at the bottom of the columns, Marc and Mira will pay a total of $7,172.81 in interest in the first year Using Technology To automate the construction of the amortization schedule in Exam ple 6 using a graphing calculator or a spreadsheet, see the Technology Guide TI-83/84 Plus and Technology Guide Spreadsheet at the end of the chapter Before We Go On Is there a formula to calculate the outstanding principal at the end of each month in Example 6? A: We can use the present value formula. After k months there are Less than a minute 54 pages left Using Technology Website www.WanerMath.com -> Online Utilities Time Value of Money Utility To find the outstanding principal after 10 years in Example 7, enter the values shown, and press "Compute" next to PV. Compute PV Compute PMT -66039 Compute Compute Compute Clear al Example Bonds (Optional) Suppose that a corporation offers a 10-year bond paying 6.5% with pay ments every 6 months. As we saw in Example 3 of Section 2.1, this means that if we pay $10,0oo for bonds with a maturity value of $10,000 , we will receive 6.5/2-3.25% , of $10,000 , or $325 , every 6 months for 10 years, at the end of which time the corporation will give us the original $10,0oo back But bonds are rarely sold at their maturity value. Rather, they are auctioned off and sold at a price the bond market determines they are worth For example, suppose that bond traders are looking for an investment that has a rate of return or yield of 7% rather than the stated 6.5% (sometimes called the coupon interest rate to distinguish it from the rate of return) How much would they be willing to pay for the bonds above with a maturity value of $10,000? Think of the bonds as an investment that will pay the owner $325 every 6 months for 10 years, and will pay an additional $10,000 on maturity at the end of the 10 years. We can treat the $325 payments as if they were an annuity and determine how much an investor would pay for Less than a minute 52 pages left Bonds (Optional) Suppose that a corporation offers a 10-year bond paying 6.5% with pay- ments every 6 months. As we saw in Example 3 of Section 2.1, this means that if we pay $10,0oo for bonds with a maturity value of $10,000 , we will receive 6.5/2-3.25% , of $10,000 , or $325 , every 6 months for 10 years, at the end of which time the corporation will give us the original $10,0oo back But bonds are rarely sold at their maturity value. Rather, they are auctioned off and sold at a price the bond market determines they are worth For example, suppose that bond traders are looking for an investment that has a rate of return or yield of 7% rather than the stated 6.5% (sometimes called the coupon interest rate to distinguish it from the rate of return) How much would they be willing to pay for the bonds above with a maturity value of $10,000? Think of the bonds as an investment that will pay the owner $325 every 6 months for 10 years, and will pay an additional $10,000 on maturity at the end of the 10 years. We can treat the $325 payments as if they were an annuity and determine how much an investor would pay for such an annuity account if it earned 7% compounded semiannually. Sepa- rately, we determine the present value of an investment worth $10,00o ten years from now, if it earned 7% compounded semiannually. For the first cal culation we use the annuity present value formula, with i - o.o7/2 and PV PMT1- 1-1 + 0.07/2) 20 325 0.07/ 2 - $4,619.03 For the second calculation we use the present value formula for compound interest: PV-10,000(1 + 0.07/2)-20 - $5,025.66 Thus, an investor looking for a 7% return will be willing to pay $4,619.03 for the semiannual payments of $325 and $5,025.66 for the $10,000 payment at the end of 10 years, for a total of $4,619.03 + 5,025.66 - $9,644.69 for the $10,000 bond Less than a minute 51 pages left

Answer 1

	1	Mortgage interest payment =(Beginning of the year Loan Balance )*Interest Rate
		Balance of the Annual payment is accounted as payment of principal
		Hence, the Beginning Balance in the next period gets reduced by the principal amount
		accounted for in the earlier period
		Thus every subsequent year, the interest payment reduces .
		Since annualpayment is contant, Principal payment in every subsequent year increases
		PREPARATION OF AMORTIZATION SCHEDULE:
		STEP 1
		Calculate constant payment per period based on mortgage amount, number of payments and interest rate
		STEP 2
		Create Mortgage schedule with the following formula:
		Interest payment =Beginning Loan balance*(Interest rate per period)
		Principal payment =(Constant Payment per period)-(Interest payment for the period)
		Ending Loan Balance of a Period =(Beginning Balance)-(Principal payment of the period)
		Beginning Loan balance of a period=Ending Loan Balance of previous period
		In this cae
	Pv	Mortgage Loan amount	$90,000
		Interest payment in month 1=90000*Interest rate	$600.00
	Rate	Monthly interest rate=600/90000=	0.0066666667
		Annual interest rate=0.006667*12=	0.08	8%
	Nper	Number of payments	360	(30*12)
		Monthly constant payment	$660.39	(Using PMT function of excel with Rate=0.00666667,Nper=360,Pv=-90000)
		Excel Command: PMT(0.00666667,360,-90000)
		MORTGAGE SCHEDULE
			A	B	C=A*0.006666667	D=B-C	E=A-D
		Month	Beginning Balance	Total Payment	Interest	Principal	Ending Balance
		0					$90,000
		1	$90,000.00	$660.39	$600.00	$60.39	$89,939.61
		2	$89,939.61	$660.39	$599.60	$60.79	$89,878.82
		3	$89,878.82	$660.39	$599.19	$61.20	$89,817.62
		4	$89,817.62	$660.39	$598.78	$61.60	$89,756.02
		5	$89,756.02	$660.39	$598.37	$62.01	$89,694.01
		6	$89,694.01	$660.39	$597.96	$62.43	$89,631.58
		7	$89,631.58	$660.39	$597.54	$62.84	$89,568.73
		8	$89,568.73	$660.39	$597.12	$63.26	$89,505.47
		9	$89,505.47	$660.39	$596.70	$63.69	$89,441.78
		10	$89,441.78	$660.39	$596.28	$64.11	$89,377.67
		11	$89,377.67	$660.39	$595.85	$64.54	$89,313.14
		12	$89,313.14	$660.39	$595.42	$64.97	$89,248.17