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### 172A 2010 Exam 1

Course: MATH 172a, Fall 2011
School: UCLA
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Word Count: 669

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172A Math Exam 1 10/22/10 Name: _______________________ 1. Deposit to fund: \$3,000 paid on 1/1/2010 Withdrawal from fund: \$1,000 on 1/1/2015 Interest accumulates at the following rates for the various periods specified: 2010 through 2012: 2013 through 2016: 2017 through 2022: d(5) = 8% = 7% i(24) =6% What is value of the fund as of 12/31/2022? Do the problem whichever way you want. If you use the TVM...

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172A Math Exam 1 10/22/10 Name: _______________________ 1. Deposit to fund: \$3,000 paid on 1/1/2010 Withdrawal from fund: \$1,000 on 1/1/2015 Interest accumulates at the following rates for the various periods specified: 2010 through 2012: 2013 through 2016: 2017 through 2022: d(5) = 8% = 7% i(24) =6% What is value of the fund as of 12/31/2022? Do the problem whichever way you want. If you use the TVM functions on your calculator, fill in the boxes below. n i PV PMT FV beg/end 2. Bank I credits interest at a continuous rate that is a function of t: (t) = (50+10t+t2)/1000 a) \$5,000 is deposited at t=2. What is the accumulated value at t=6 ? b) What is the annual rate of simple interest earned during the investment period? 3. Anthony opened a savings account at Bank Z on 7/1/2010. It credits interest at a nominal rate of 8% compounded quarterly. He made the following deposits and withdrawals. Deposits: 7/1/2010 \$500, 7/1/2014 \$200 Withdrawals: 7/1/2012 \$100, 7/1/2015 \$X, 7/1/2018 \$865 The 7/1/2018 withdrawal emptied the account. 1) Draw a timeline of the cashflows in and out of the account 2) Calculate X to 2 decimal places, if you use the calculator functions, be sure to show all entries n i PV PMT FV beg/end 4. Anne and Frank each borrow \$12,000 from their father. Anne repays her loan with two payments: \$6,000 in 2 years and \$8,000 in 4 years Frank prefers to make a single payment of \$15,000. When should Frank make the payment so that he and Anne will each have the same effective interest rate? n i PV PMT FV beg/end 4. Kristina opened a savings account on 1/1/2007 and made the following deposits: 1/1/2007: \$2,500; 1/1/2012: \$900 She made the following withdrawals: 1/1/2011: \$700; 1/1/2015: \$500 Her account balance on 12/31/2016 is \$5,000 a. Show on a timeline the cash flows in and out of this account. b. What was the effective annual rate of interest (IRR) Kristina earned in this account from 1/1/2007 to 12/31/2016? c. If the Bank had promised an interest rate of 5% compounded annually, what would be the account balance on 12/31/2016? 5. An investor pays \$100,000 today for a investment that returns cash flows of \$70,000 at end of year 3 and \$50,000 end at of year 4, half of year 3s cash flow is invested in a two-year Certificate of Deposit (CD) to earn 8% per annum effective and all of year 4s cash flow is invested in a one-year CD to earn 7% per annum effective. All monies are withdrawn by t=5 If i = 5%, what is the Net Present Value (NPV) of this investment today? 6. Daniel opens an account at Bank B that credits interest at i(4)=6% and deposits \$10,000 He makes the following annual withdrawals starting at t=1: \$X for 1 year, followed by \$2X for 2 years, followed by \$4X for 4 years At t=8, he still has \$2,500 left in his account. Calculate X n i PV PMT FV beg/end 7. Values of Fund: Date Balance 12/31/09 10,000 3/31/10 12,000 6/30/10 14,000 Deposits: \$4,000 (1/1/10); \$1,500 (1/2/10); 12/31/10 X \$2,000 (4/1/10) Withdrawals 9/30/10 15,000 \$250 (4/2/10) The dollar-weighted rate of return for 2010 is 10%. What is the time-weighted rate of return for 2010? In your calculation, you can ignore the effect of one or 2 days of timing differences. Also, for dollar-weighted calculation, you can use either simple or compound interest. 8. Given: s2n = vn 42.13229 = .49662 Solve for n n i PV PMT FV beg/end 9. At an annual effective interest rate of i, the PV of a perpetuity paying \$15 every 2 years equals \$124, with the first payment at the end of year 6. Using the same interest rate i, calculate the PV of a perpetuity that pays \$2 every quarter, with the first payment 1 year from now. 9. Mr. Rich creates an endowment that will pay out \$100,000 at the end of each year in perpetuity. The first n payments will go to charity A and the next 2n payments will go to Charity B, after that, all remaining payments will go to Charity C. The PV of Charity Cs share is \$438,656 and represents one-third of the value of the endowment. Calculate the PV of As and Bs share respectively. n i PV PMT FV beg/end 10. Interest is credited under the investment year Method according to the following table: Marcella made the following deposits: 1/1/1989 \$1,000 1/1/1992 \$1,500 1/1/1993 \$500 a) What is the value of her account on 12/31/1994 b) What is level annual effective rate of interest she earned from 1/1/89 to 12/31/94?
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