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# Math 98: Fianncial MathDecal - Study Guide Math 98

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This 4 page Study Guide was uploaded by Tom McCaleb on Saturday October 11, 2014. The Study Guide belongs to Math 98 at University of California Berkeley taught by Sunny in Fall. Since its upload, it has received 236 views. For similar materials see Fianncial MathDecal in Finance at University of California Berkeley.

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Date Created: 10/11/14

Fall 2014 Decal FM Midterm Oct 6 2014 Name SID The present value of a 25year annuity immediate with a first payment of 2500 and decreasing by X each year thereafter is 15923 The armual effective rate of interest is 10 Determine X A 70 B 80 C 90 D 100 E 110 You are given the following table of interest rates Calendar Year of Portfolio Original Rates Investment Investment Year Rates in in y ii 1393 134 ii Pv i 39 5 1992 825 825 840 850 850 835 1993 850 870 875 890 900 860 1994 900 900 910 910 920 885 1995 900 910 920 930 940 910 1996 925 935 950 955 960 935 1997 950 950 960 970 970 1998 1000 1000 990 980 1999 1000 980 970 2000 950 950 2001 900 A person deposits 1000 on January 1 1997 Let the following be the accumulated value of the 1000 on January 1 2000 P under the investment year method Q under the portfolio yield method Calculate P Q C 2610 D 2655 E 2700 A loan is repaid with 10 annual payments The rst payment occurs one year after the loan The rst payment is 100 and each subsequent payment increases by 10 The annual effective rate of interest is 5 The amount of principal repaid in the 4th payment is X Determine X A 71 B 76 C 80 D 84 E 91 10 deposits of 2000 are made every other year with the first deposit made immediately The resulting fund is used to buy a perpetuity with payments made once every 3 years following the pattern X 4X 7X 10X The rst perpetuity payment is made 3 years after the last deposit of 2000 The annual effective rate of interest is 6 Determine X A 408 B 458 C 471 D 512 E 603 5 A fairly smart actuary also know as an FSA is offered the following rates on a loan 1 X nominal annual rate of interest compounded monthly X nominal annual rate of discount compounded monthly X annual effective rate of interest X annual effective rate of discount Cflrhbilxb X constant force of interest Which rate does the FSA take A1 B2 C3 D4 E5 6 An armuity pays 1 at the beginning of each year for 71 years Using an annual effective interest rate of 239 the present value of the annuity at time 0 is 855948 It is also known that 1 7quot 3172169 Find the accumulated value of the annuity immediately after the last payment A 27152 B 28456 C 29324 D 30765 E 31973 7 Deposits are made at the beginning of every month into a fund earning a nominal annual rate of 6 convertible monthly The rst deposit is 100 and deposit increase 2 every year In other words deposits 112 are 100 deposits 1324 are 100 x 102 102 deposits 2536 are 100 x 1022 10404 and so on Calculate the md balance at the end of 10 years A 16569 B 16893 C 17257 D 17770 E 17859 8 On January 1 a fund has a balance of 100 Sometime during the year a withdrawal of 20 is made Immediately before the withdrawal the fund balance is 110 At year end the balance is 95 If the time weighted and dollar weighted rates for the year are equal then in what month was the 20 withdrawal made A June B July C August D September E October 9 A fund earns simple interest of i which of the following are true 1 The effective rate of interest is constant for each period 2 The amount of interest is constant for each period 3 The equivalent force of interest is ln1i A 1 only 10 B 2 only C 3 only D 2 and 3 only E none ofthe above You are given the following information about 3 funds Effective Rate Fund per Year Interest Payments A j paid directly to investor B 5 paid directly to investor C 4 automatically reinvested An investor deposits 10000 into fund A He reinvests fund A s interest payments into fund B He reinvests fund B s interest payments into fund C The total value of all three funds after 10 years is 20000 Determine j A6 1 1 At the beginning of the year an investment fund Was established with an initial deposit of 1000 A new deposit of 1000 Was made at the end of 4 months Withdrawals of 200 and 500 were made at the end of 6 months and 8 months respectively The amount in the fund at the end of the year is 1560 Calculate the dollarWeighted moneyWeighted yield rate earned by the fund during the year A 1857 B 2000 C 2261 D 2600 E 2889 12 A 10000 loan is repaid with level annual payments The rst payment is made one year after taking out the loan The outstanding balance just after the 8th payment is 711210 The outstanding balance just after the 16th payment is 284536 Calculate the outstanding balance just after the 17th payment A 1185 B 1485 C 1885 D 1985 E 2185 13 At an annual effective interest rate 239 i 1 grows to 5 in 1 years ii 2 grows to 8 in 3 years iii 3 grows to 20 in z years Calculate l21 z393 21quot39 A 625 B 650 C 675 D 700 E 725 14 A corporation borrows 10000 for 25 years at an armual effective interest rate of 5 A sinking fund is used to accumulate the principal by means of 25 annual deposits earning an effective annual interest rate of 4 Calculate the sum of the net amount of interest paid in the 12th installment and the increment in the sinking fund for the 8th year A 676 B 686 C 696 D 706 E 716 15 1 Let6t 05t15 4t What is the first year for which the effective rate of discount is less than 125 A3 B4 C5 D6 E7

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