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FIN CHAP 06 SOLUTIONS complete

FIN CHAP 06 SOLUTIONS complete - CHAPTER 6 6-1 FUTURE VALUE...

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CHAPTER 6 6-1 FUTURE VALUE If you deposit \$10,000 in a bank account that pays 10 percent interest annually, HOW MUCH MONEY WILL BE IN YOUR ACCOUNT AFTER 5 YEARS? 0 10% 1 2 3 4 5 PV = 10,000 FV 5 = ? FV n = PV (1 + i) n FV 5 = \$10,000(1.10) 5 = \$10,000(1.61051) = \$16,105.10 ALTERNATIVELY, WITH A FINANCIAL CALCULATOR ENTER THE FOLLOWING: N = 5 I = 10 PV = -10,000 Now, solve for FV FV = \$16,105.10.

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6-2 PRESENT VALUE Assume that you can earn 7 percent if you were to invest in other securities of equal risk. WHAT IS THE PRESENT VALUE OF A SECURITY THAT PROMISES TO PAY YOU \$5,000 IN 20 YEARS? 0 7% 1 2 3 …….. 20 PV = ? FV 20 = 5,000 PV = ( 29 n n i FV + 1 PV = ( 29 20 07 . 1 5000 PV = \$1,292.095 or \$1,292.10 WITH A FINANCIAL CALCULATOR ENTER THE FOLLOWING: N = 20 I = 7 FV = 5,000. Now, solve for PV PV = \$1,292.10
6-3 TIME FOR A LUMP SUM TO DOUBLE If you deposit money today into an account that pays 6.5 percent interest, HOW LONG WILL IT TAKE FOR YOU TO DOUBLE YOUR MONEY? 0 6.5% 1 2 3 ……. n = ? PV = 1 FV n = 2 FV n = PV (1 + i) n 2 = 1(1.065) n 2 = 1.065 n Note: this problem can be solved (which I am not requiring you to do) by taking the natural log of both sides of the equation: ln 2 = n ln 1.065 n = __ln 2___ ln 1.065 n = .6931 .0630 n = 11.006 WITH A FINANCIAL CALCULATOR ENTER THE FOLLOWING: I = 6.5 PV = -1 PMT = 0 FV = 2 Now, solve for N N = 11.01 11 years (note: because of internal programming some calculators will round up to 12)

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6-4 REACHING A FINANCIAL GOAL John Roberts has \$42,180.53 in a brokerage account, and he plans to contribute an additional \$5,000 to the account at the end of every year. The brokerage account has an expected annual return of 12 percent. IF JOHN’S GOAL IS TO ACCUMULATE \$250,000 IN THE ACCOUNT, HOW MANY YEARS WILL IT TAKE FOR JOHN TO REACH HIS GOAL? 0 12% 1 2 3 …….. n = ? PV = 42,180.53 5000 5000 5000 FV = 250,000 FV = PV (1 + i ) n + PMT = - + n t t n i 1 ) 1 ( \$250,000 = \$42,180.53 (1 + i ) n + 5,000 = - + n t t n i 1 ) 1 ( \$250,000 = \$42,180.53 (1.12 ) n + 5,000 = n t 1 ( 29 t n - 12 . 1 USING YOUR FINANCIAL CALCULATOR, ENTER THE FOLLOWING DATA: I = 12 PV = -42,180.53 (outflow) PMT = -5,000 (outflow) FV = 250,000 N = ? Solve for N…….. N = 11 Therefore, it will take 11 years for John to accumulate \$250,000. Note: to check your answer mathematically, you can plug n = 11 into the data above and solve for FV, e.g., FV = \$42,180.53 (1.12 ) 11 + 5,000 = n t 1 ( 29 t n - 12 . 1 FV = \$146,727.082 + \$103,272.92 = \$250,000
6-5 EFFECTIVE RATE OF INTEREST Your parents are planning to retire in 18 years. They currently have \$250,000, and they would like to have \$1,000,000 when they retire. WHAT ANNUAL RATE OF INTEREST WOULD THEY HAVE TO EARN ON THEIR \$250,000 IN ORDER TO REACH THEIR GOAL, ASSUMING THEY SAVE NO MORE MONEY? 0 i = ? 1 2 3 …………. 18 PV = 250,000 FV 18 = 1,000,000 FV = PV (1 + i) n \$1,000,000 = \$250,000 (1 + i) 18 WITH A FINANCIAL CALCULATOR ENTER THE FOLLOWING: N = 18 PMT = 0 PV = -250,000 FV = 1,000,000 Now, solve for I I = 8.01% 8%.

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6-6 FUTURE VALE OF AN ANNUITY WHAT IS THE FUTURE VALUE OF A 5-YEAR ORDINARY ANNUITY THAT PROMISES TO PAY YOU \$300 EACH YEAR? THE RATE OF INTEREST IS 7 PERCENT. 0 7% 1 2 3 4 5 300 300 300 300 300 FV 5 = ? FVA n = PMT (1 + i) 1 - n + PMT (1 + i) 2 - n + PMT (1 + i) 3 - n …. + PMT (1 + i) n FVA 5 = PMT = - + n t t n i 1 ) 1 ( FVA 5 = 300 = - 5 1 5 ) 07 . 1 ( t t FVA 5 = \$1,725.22 WITH A FINANCIAL CALCULATOR ENTER THE FOLLOWING: N = 5 I = 7 PV = 0 PMT = -300 Now, solve for FV FVA = \$1,725.22.
6-7 FUTURE VALUE OF AN ANNUITY DUE WHAT IS THE FUTURE VALUE OF A 5-YEAR ANNUITY DUE THAT PROMISES TO PAY YOU \$300 EACH YEAR? ASSUME THAT ALL PAYMENTS ARE REINVESTED AT 7 PERCENT A YEAR, UNTIL YEAR 5.

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