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For example, say you want to determine how many years it will take for you to accumulate $1,000,000 by saving $500 per month at 10% E. growth per annum.

P/Y = 12 I/Y= 10 PMT= -500 FV = 1000000 Solve N= 345.0922 MONTHS DIVIDE BY 12 =28.758 YEARS
If you stand to inherit $100,000 in 10 years, what is it worth now at a 10% discount rate? P/Y = 1 N = 10 I/Y= 10 FV=100000 Solve PV = 35174.82

1. You want to lease a new Taurus. The sticker is $20,000. Tax and title is $1250. The lease term is 3 years. The loan APR interest rate is 6%. The depreciation is 18% in year 1, 12% in year 2 and 10% in year 3. The cap cost reduction (increase in cost) is $500. CALCULATE LEASE PAYMENT
NOTE: Depreciation is computed by taking the accumulated % depreciation over the least term (3 years in this case) and multiplying it times net investment (cost + tax & title + dealer prep + freight) P/Y = 12 N = 36 I/Y = 6 PV = -$21750 FV = 12000 SOLVE PMT= $354.84

2. Assume you negotiate the price on problem 1 to $19000. Tax and title are $1200. Cap cost is $500. You get financing at a good rate of 2.9%. CALCULATE NEW PAYMENT. PV = -$20700 I/Y = 2.9 FV=12000 N=36 SOLVE FOR PMT = $280.94

3. Lease a new Camry. Sticker $20,500. You negotiate price of $19500. Tax and title = $1300. Depeciation = 15% yr 1, 10% yr. 2 and 8% yr. 3. I/Y = 2.9%. Cap cost reduction is $500. CALCULATE LEASE PAYMENT. Residual = $13735 I/Y = 2.9 Cap cost reduction= $500 PV = -$21300FV = $13735 The Camry costs $500 more but the residual is $1174 higher (Foreign cars do not depreciate as much as U.S. cars) PMT = $252.25 (SAVINGS OF 10% even though the Camry cost more up front.)

4. Lease a Camry. Same facts as # 3 except I/Y = 8%. SOLVE FOR PMT. EXCEPT I/Y = 8 PV = -21300 FV = 13735 N = 36 SOLVE FOR PMT = $326.44

5. Same as 4. You trade in your old car for $5000. SOLVE FOR PMT. PV = -16300 FV = 13735 N = 36 SOLVE FOR PMT = $170.81

6. You need retirement income of $2500 per month. You plan to retire at age 55. Your actuarial life expectancy is 85. HOW MUCH MONEY WILL YOU NEED AT AGE 55 TO FUND THIS RETIREMENT ANNUITY ASSUMING AN 8% INVESTMENT RETURN DURING RETIREMENT. SET END. P/Y = 12 I/Y = 8 PMT = $2500 N = 30 X 12 = 360 FV = 0 SOLVE FOR PV = -$344,236

7. How much will you need to save EACH MONTH in problem 6 above assuming an investment return BEFORE RETIREMENT from age 25 to age 55 (30 YEARS) ASSUMING A 10% INVESTMENT RETURN PRIOR TO RETIREMENT. SET END. P/Y = 12 N = 360 I/Y = 10 FV = $344,236 (do not enter this as negative) SOLVE FOR PMT = -$151.03
8. You have a child age 4. You need to save for college. The cost of college in a public university if $9000 per year in current dollars. Your estimated investment return is 8%. College costs are rising at 6%. CALCULATE.THE TOTAL COST OF A COLLEGE EDUCATION IN A PUBLIC UNIVERSITY FOR THIS CHILD BEGINNING AT AGE 18 FOR 4 YEARS. STEP ONE: Calculate annual cost in YEAR 14 AT 6% inflation. SET BGN:N=14 P/Y = 1 I/Y = 6 PV = -9000 SOLVE FOR FV. This is college cost in year 14. FV =20348.13 STEP TWO: Calculate annual cost of college (year 14-17) FRESHMAN YR 14 $20348.13 SOPHOMORE YR 15 $21569.02 (YR 1 x 1.06) JUNIOR YR 16 $22863.17 (YR 2 x 1.06) SENIOR YR 17 $24234.96 (YR 3 x 1.06 TOTAL COST – 4 YEARS $89015.28 STEP THREE: Calculate how much you need to save each month to accumulate enough funds to meet total dollar need in step two. Use I/Y of 8%. P/Y = 12 N = 168 I/Y = 8 PV = 0 FV =$ 89015.28 SOLVE FOR PMT PMT = -$ 287.07 SAVINGS / MONTH --1 CHILD Save for 14 years (168 months) at assumed return of 8%
9. You want to buy a home costing $200,000. You plan to put 20% down. The loan cost includes 2 POINTS which ar added to principal at closing. The rate is 7.25% for a 30 year mortgage and 6.85% for a 15 year mortgage. CALCULATE PAYMENT FOR A 30 AND 15 YEAR LOAN. HOME PRICE=$200,000 [COST = PRICE (1- DN PMT) + POINTS AND CLOSING COSTS] = MORTGAGE LOAN = $160,000 (this is an outflow)
DOWN PAYMENT = 20% POINTS = 2 = 2% 0F LOAN P/Y = 12 ( 1 Point is 1% of LOAN) 2 points = $3200.
15 YEAR MORTGAGE N = 180 I/Y = 6.85% SET BGN solve for PMT: 30 year $1106.62 15 year $1444.99 ($338.37 / mo more)
31% higher payment paid off 50% faster A simple strategy is to pay an additional $338 per month (applied to principal) when you can to amortize the loan.

10. YUPPIE MORTGAGE. Use the facts of the problem 9 above for a 30 year mortgage. Assume payments are made every 2 weeks (26 times per year – 52/2 = 26). Solve for N and divide by 26 to determine the years to pay off this “30 year” mortgage. PMT = 1106.62/2 OR $553.31 BI-WEEKLY
Set P/Y to 26 (52/2) Most people will not notice the difference especially if they get paid bi-weekly I/Y = 7.25 PV = -$163200 PMT = $553.31 SOLVE N = 616.2 PMTS Divide by 26 =23.7 Years RESULT: A reduction in term of 6.3 years or 21% IF YOU TAKE OUT A MORTGAGE AT AGE 30 IT WILL BE PAID OFF WHEN YOU ARE ALMOST 54.

11. You want to retire in 15 years. You need an annual income of $75000 in income at retirement and do not wish to touch principal. You plan to save $500 per month. You currently have a small portfolio worth $100,000. What annual interest return (I/Y) must you achieve in order to reach this goal? HINT: FV = $75,000 / .5%. STEP 1: We much calculate the size of the portfolio needed to produce the income.
75000/.05 = $1,500,000 THIS IS FV TVM - INVESTING CONTD. SOLUTIONS STEP 2: WE ARE SOLVING FOR I/Y P/Y =12 NOTE: since you are saving MONTHLY, you must set P/Y to 12 N = 15 X 12 = 180 PV = -100000 PMT = -500 FV = 1500000 SOLVE FOR I/Y = 16.20%

12. USING BOND SPREADSHEET (covered later in course). You want to buy an A rated bond that matures in 15 years. The coupon rate is 8%. The yield on A rated bonds in the same maturity range is 7.5%. What price would you pay for this bond? Corporate bonds mature at PAR. Par = $1000 • Corporate bonds pay interest coupons SEMIANNUALLY. P/Y = 2 • The stated interest rate on the bond is fixed for the life of the bond. This is called the “Coupon rate.” • All bonds are priced to the market yield on bonds of similar type, quality and maturity. This yield is always changing and bonds adjust to it by the price fluctuating. If yields in the market go UP, bond prices go DOWN.
SET BGN SET P/Y = 2 N = 30 (Remember N = P/Y times the number of years) I/Y = 7.5 In a bond problem I/Y is the yield on other similar bonds. DO NOT use the coupon rate on the bond. FV = 1000 All bonds mature at par. Par = 1000 PMT = 40 Bonds pay interest semiannually. This bond has a coupon rate of 8%. Annual interest = 8% x $1000 = $80 Each coupon is therefore half the annual interest of $80 or $40 SOLVE FOR PV 1071.32
PROBLEM A loan of $50,000 is due 10 years from today. The borrower wants to make annual payments at the end of each year into a sinking fund that will earn interest at an annual rate of 10 percent. What will the annual payments have to be?

Suppose that the borrower will make monthly payments that earn 10 percent interest, compounded monthly. How much will he pay annually into the fund? With annual compounding: P/Y = 1, N = 10, I = 10, PV = 0, FV = 50,000 ( PMT = ( $3,137.27.

With monthly compounding: P/Y = 12, N = 10 ( 12 = 120, ( PMT = ( 244.09. These are monthly payments, so the total annual payment will be 244.09 ( 12 = $2,929.04.

PROBLEM Suppose you have the opportunity to make an investment in a real estate venture that expects to pay investors $750 at the end of each month for the next eight years. You believe that a reasonable return on your investment should be 17 percent compounded monthly.

How much should you pay for the investment? P/Y = 12, N = 8 ( 12 = 96, I = 17, PMT = 750, FV = 0 ( ( $39,222.96.

What will be the total sum of cash you will receive over the next eight years? This can be solved by setting I = 0, PV = 0, and computing FV = ( $72,000. Notice that the sign of this solution is negative because the payments have been entered as positive values.

Why is there such a large difference between (a) and (b)?The difference between the answers in parts (a) and (b) represents the foregone interest that results from receiving the payments in the future, rather than today.

PROBLEM An investor can make an investment in a real estate development and receive an expected cash return of $45,000 after six years. Based on a careful study of other investment alternatives, she believes that an 18 percent annual return compounded quarterly is a reasonable return to earn on this investment. How much should she pay for it today? P/Y = 4, N = 6 ( 4 = 24, I = 18, PMT = 0, FV = 45,000 ( PV = ( $15,646.66.…...

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