Math 441 Midterm 1 Review Solutions

Math 441/497FM - Midterm 1 Review Solution Set Problem 1 (practice Exam 3, Problem 6 from the book): Assume that the initial deposit was equal to 1. Now find the future value of the deposit by the end of year 10. FV = 1 * I1 +

0.06 12*4 M * 12

e0.05*6 = 1.7150

Now, the textbook's solution reccomends putting this directly into terms of a nominal discount rate d convertible quarterly. I find it more intuitive to convert it to it's respective quarterly interest rate, then convert that to a nominal discount rate convertible quarterly. To do so, start by using your calculator to find the equivalent quarterly interest rate. N = 40 , PV = 1, FV =1.7150, PMT = 0, CPT [ I/Y ] = 1.357666 % = iquarterly Now convert the quarterly interest rate to a quarterly discount rate using the formula: d =

i 1+i

0.013577666 1.01357666

dquarterly =

= .013395

Keep in mind that this is still a quarterly discount rate. To put it into nominal annual convertible quarterly form, simply multiply by 4 d H4L = dquarterly * 4 = .013395 * 4 = .053579 » 5.4 % This gives answer (C)

Problem 2 (Brett's problem) First, find out what Mike's deposit grew to by year 15. Assume his initial deposit was equal to 1. FVm = 1 * I1 +

0.12 10*2 M * 2

2

15 Ht-10L

Ù 10

e

100

ât

KK15-

= 3.207 * e

152 10

+

153 300

O- K10-

102 10

+

103 300

OO

= 3.207 * 1.517 = 4.865

FVm = 2.039 Now determine an equivalent annual rate using the calculator. N = 15, PV = -1, FV = 4.865, PMT = 0, CPT [ I/Y ] = 11.123% i ≈ 11.123% Now determine what this will grow to in 25 years. N = 25, I/Y = 11.123, PV = -1, PMT = 0, CPT [FV] = 13.96 This means that his final balance will be 13.96 times his initial deposit. This gives answer (A)

Problem 3 (practice exam 4, problem 11 from book) We first need to find the principal balance due after the third payment. Using the calculator set N = 3, I/Y = 7.6, PV = 50,000 and PMT = -3000. Then CPT FV = -52,587.02. The new balance is 52,587.02. To get the new payments set N = 7, I/Y =7.6, PV = -52,587.02 and FV = 0. Then CPT PMT = 9962.76. This gives answer (C)

Printed by Mathematica for Students

2

Math 441 Midterm 1 Review Solutions.nb

Problem 4 (practice exam 3, problem 13 from book) The present value of Tom's annuity is 10 HIaL10 = 100B

Iä - 10 Ν10 M i

F = 3582.84

The present value of Jerry's annuity is X

X

J 10 N HDaL10 = J 10 NB X=

3582.84 4.325

In - a10 M i

F = 4.325 X

= 828.4

Problem 5 (practice exam 3, problem 2 from book) The price of this bond is 1035. To get the yield using the BA II Plus calculator set N = 20, PV = -1035, PMT = 30, and FV = 1000. Then CPT I/Y = 2.77%. Yield is 5.54%

Problem 6 (practice exam 4, problem 5 from book) To find the price of the bond with the calculator set N = 40, I/Y = 2.8, PMT = 30, FV = 1000. Then CPT PV =-1047.76. The accumulation of coupon payments plus interest is A = 30 A S20 0.025 H1.027L20 + S20 0.027 E = 2087.66 Total accumulation is 3087.66 1

3087.66

Annual yield = J 1047.76 N 20 - 1 = 0.056

Problem 7 (practice exam 5, problem 1 from book) To get the orginial payments set N = 360, I/Y = 0.45, FV = 100,000, and PV = 0. Then CPT PMT = -111.53. To get the accumulation after 10 years reset N = 120 and CPT FV = 17,694.47 Now set N = 240, I/Y = 0.55, PV = -17694.47, and FV = 100,000 Then CPT PMT = -68.50

Problem 8 (practice exam 6, problem 16 from book) First, we know that the outstanding balance after the fifth payment is 4506.74. We could use this to find the payment amount by treating it as a four year loan amount. 4506.74 = PmtHa4 0.08 L Pmt = 1360.6786 Now that we know the payment amount, we could solve for the initial loan amount by solving for a present value: PV = 1360.68 Ha9 0.08 L PV = 8500.02 Now we can solve for the interest portion of the first payment: I1 = 8500.02 * 0.08 = 680.00 If the interest portion of the payment is 680, the principal portion must be 680.68. Note: the solutions for Pmt and PV above can be done entirely on the BA II Plus to save time.


Math 441 Midterm 1 Review Solutions.nb

Problem 9 (Brett's problem) The net present value of Brett's tin-foil sculpture project at 10% is -40 000 +

20 000 1.1

40 000

+

1.12

= 11 239.67

(This can also be found on the BA II Plus using the NPV function on the calculator with CF0 = -40 000, C01 = 20 000, C02 = 40 000, and I = 10 The net present value of Mike's tin-foil bicycle project is 20 000 + Thus, 20 000 +

40 000 1.1

40 000 1.1

-

-

X 1.12 X

1.12

= 11 239.67 X = 54 600

Problem 10 (module 5, problem 7 from book) The equation of value here is 364.46 = 100 + 200 Ν + 100 Ν2 Thus you only need to solve the quadratic 0 = -264.46 + 200Ν + 100Ν2 The root is Ν = .90908 give i = .10 Alternatively, use the cashflow sequence (264.46, 200, 100) in the cashflow worksheet.


3