# ORIE_350_Homework__7_Answers - ORIE 350 Homework#7 Time...

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ORIE 350 Homework #7 Time Value of Money 1. Alex Trabeck opens a savings account at CFCU. The advertised APR is 3.45%, compounded monthly. If he deposits \$20,000 today, what will the balance be in the account 30 months from now, assuming no other deposits or withdrawals? ( 29 ( 29 002831 . 0 1 0345 . 1 1 1 12 1 1 = - = - + = c APR i ( 29 ( 29 89 . 769 , 21 \$ 002831 . 1 000 , 20 1 30 = = + = n i PV FV 2. You have just made a \$10,000 deposit to your savings account. Your rich aunt will make an additional deposit of \$8,000 to your account one year from now. Assuming you earn an annual nominal interest rate of 4%, compounded monthly, and make no additional contributions, what will your account be worth 4 years from today? The \$10,000 deposit earns interest for 48 months; the \$8,000 deposit earns interest for 36 months. The interest rate per month is 0.04/12 = 0.003333. ( 29 ( 29 ( 29 n 48 36 FV PV 1 i 10,000 1.003333 8,000 1.003333 \$20,750.16 = + = + = 3. An investment pays you 15 annual payments of \$40,000, with the first payment occurring 11 years from now. Recall that the compounding frequency equals the payment frequency unless explicitly stated otherwise. a. If the annual nominal interest rate is 7%, then what is the value of the investment today? ( 29 ( 29 n 15 10 1 1 i 1 1.07 PV A 40,000 \$364,316.56 i 0.07 - - - + - = = = ( 29 10 0 10 PV PV \$185,200.07 1.07 = = b. What is the value of a similar investment, with identical terms except the annuity extends for 20 years, instead of 15 years? ( 29 ( 29 n 20 10 1 1 i 1 1.07 PV A 40,000 \$423,760.57 i 0.07 - - - + - = = = ( 29 10 0 10 PV PV \$215,418.39 1.07 = =

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4. Gina Davis deposits \$30,000 in an investment account earning an annual, nominal rate of 5.2%. Interest is compounded monthly. How long will Gina have to wait if he wants
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