Chapter 4 - Level 1 - Course FM Solutions

Transcription

1 ONLY CERTAIN PROBLEMS HAVE SOLUTIONS. THE REMAINING WILL BE ADDED OVER TIME. 1. (F12H4) Michael has taken a loan and has agreed to repay it with monthly payments for 25 years. The monthly payments in the first year are 25. The monthly payments in the second year are 5. The monthly payments continue to increase each year by 25 until monthly payments of 625 are made during the 25 th year. The interest rate on Michael s loan is 8% compounded monthly. Calculate the amount of Michael s loan. a b. 26, c. 29, d. 48,93.99 e. 335,84.3 a /12 v $

2 2. (F11P2) A perpetuity makes payments at the end of each quarter. The payments in the first year are 2 per quarter. The payments in the second year are 4 per quarter. The payments in the third year are 6 per quarter. The payments each year continue to increase in the same pattern. Calculate the present value of this perpetuity using an rate of 12% compounded quarterly. a. 14, b. 59, c. 61,577.3 d. 62,222,22 e. 228, a v $59,783.79

3 3. (F11P2) A perpetuity due make monthly payments of in the first year. It makes monthly payments of 2 in the second year. The monthly payments in the third year are 3. The payments continue to increase in the same pattern. Calculate the present value of this perpetuity due at an annual rate of interest of 6%. a. 36, b. 36, c. 38, d. 424, e. 426, a v 6 1/ / $36, /12 1/12 4. (S12P4) A year continuous annuity pays at a rate of t at time t. If v t =.94 t, calculate the accumulated value of the annuity after ten years. a b c d e e t.94 t e ( Ia) ( Ia) ( ) ( ) I s I a e (d) (.94 )

4 5. (S12H4) A continuous annuity for 6.5 years pays at a rate of 2 The discount function for this annuity is v( t) 1.2t. 2 2t 1 at time t. Calculate the present value of the annuity. a b c d e (2 1)(1.2 ) ( ) t 5 t t ( (6.5) (6.5) 6.5) () t t dt t t dt

5 6. (F11P2) A continuous 2-year annuity pays at a rate of 4t 4 at time t. You are given that a(t) = (1.1t 2 ) -2 Calculate the present value of this annuity. a.,349,241 b. 12,32,23 c. 13,246,984 d. 13,321,123 e. 14,129, (4 (1.1 )(1.1 )) (4 (1.2.1 )) (4.8.4 ) t t t (8(2) (2) (2) ) () t t t dt t t t dt t t t dt

6 7. (F11P2) A continuous 2-year annuity pays at a rate of 2t 2 at time t. You are given that a(t) = (1.3t) -1 Calculate the accumulated value of this annuity. a. 29, b. 34,92.23 c. 56,32.12 d. 65,232.4 e. 73, (2 (1.3 )) t t dt (2.6 ) t t dt t 4t (2) (2) (1.3(2)) (2.5) (FMP7) If δ =.6, calculate. a b c d e. 13.7

7 9. (FMP7) A 2 year annuity pays at the beginning of each quarter during the first year, 2 at the beginning of each quarter during the second year, etc with 2 being paid at the beginning of each quarter during the last year. Calculate the present value of the annuity assuming an annual effective interest rate of 12%. a. 185 b c d. 219 e (FMP7) A 2 year annuity pays at the beginning of each quarter during the first year, 2 at the beginning of each quarter during the second year, etc with 2 being paid at the beginning of each quarter during the last year. Calculate the accumulated value of the annuity assuming a nominal interest rate of 6% compounded monthly. a. 11,579 b. 11,754 c. 12,917 d. 13,112 e. 13, (FMP7) A perpetuity paid continuously at a rate of per year has a present value of 8.. Calculate the annual effective interest rate used to calculate the present value. a. 11.8% b. 12.1% c. 12.5% d. 12.9% e. 13.3% 12. (FMP7) If δ =.6, calculate the present value of a continuous annuity of 1 payable for 2 years. a b c d e. 12.5

8 13. (FMP7) If i =.4, calculate the accumulated value of a continuous annuity payable at a rate of per year for years. a b. 121 c d. 123 e (FMP7) If δ =.6, calculate the present value of year continuous annuity payable at a rate of s at time s. a b c d e (S9Q3)A 3 year annuity immediate pays 5 each quarter of the first year. It pays each quarter of the second year. The payments continue to increase annually so that the payments in each quarter are 5 higher than the previous year. Calculate the present value of this annuity at an annual effective interest rate of %. a. 13,48.89 b. 14, c. 15, d. 17, e. 68,756.15

9 16. Calculate the present value of this annuity at a nominal rate of % compounded quarterly. a. 13,256.2 b. 14,32.54 c. 15,17.75 d. 17,67.43 e. 17,936.59

10 17. (S9Q3)An annuity due makes monthly payments for 15 years. The first payment is. Each subsequent payment is larger than the previous payment. In other words, the payment at the start of the second month is 2 and the payment at the start of the third month is 3, etc. a. 4, b. 54, c. 54, d. 56, e. 57,518.99

11 18. (S12HW) Brian is receiving payments from an annuity. The payments are made continuously at a rate of t at time t for the next ten years. Calculate the present value of this annuity if the interest rate is 5% compounded continuously. a b c d. 5. e Ia a nv n n.5 n.5 1i e 1 e (.5).5 a v e.5 Ia (S12HW) Neal is receiving continuous payments under a perpetuity that pays t at time t. Calculate the present value of this perpetuity at annual effective rate of interest of 12%. a b c. 69, d. 77,861.6 e. 89, Ia 2 ln(1.12) 1 Ia ln(1.12) 2