Exercise 5.20 Consider the following portfolio of annuities-due currently being paid from the assets of a pension fund. Age Number of annuitants 60 40 70 30 80 10 Each annuity has an annual payment of $10000. The lives are assumed to be independent. Assume mortality follows the Standard Ultimate Life Table, with interest at 5% per year. Calculate (a) the expected present value of the total outgo on annuities, (b) the standard deviation of the present value of the total outgo on annu- ities, and (c) the 95th percentile of the distribution of the present value of the total outgo on annuities, using a Normal approximation.

For the following amount at the given interest rate compounded​ continuously, find​ (a) the future value after 6 ​years, (b) the effective​ rate, and​ (c) the time to reach ​$13,000. $5600 at 3.9​% a. The future value after 6 years is approximately ​$__. ​(Do not round until the final answer. Then round to the nearest cent as​ needed.)   b. The effective rate  __%. ​(Do not round until the final answer. Then round to two decimal places as​ needed.   c. The time to reach ​$13,000 from ​$5600 at 3.9​% compounded continuously is __ years. ​(Do not round until the final answer. Then round to two decimal places as​ needed.)

Compute the simple interest INT for the specified length of time and the future value FV at the end of that time (in dollars). Round all answers to the nearest cent. $14,800 is invested for 7 months at 7% per year. INT = FV = $ $

5. Determine the value of each investment. a) $875 at 4% per year, compounded quarterly, for 5 years b) $1150 at 6% per year, compounded semi-annually, for 8 years

The annual interest rate of Jackie's savings account is 6,4%, and simple interest is calculated semiannually. What is the periodic interest rate of jackies account? 1.6% 0.53% 1.07% 3.2%

Lars has been approved for a $420,000, 20-year mortgage with an APR of 5.125%.

10 deposits increasing at a rate of 3% in size are to be made into a savings account at the end of each month. The size of the first payment is $560. Find the size of the last deposit, total accumulated value and the amount of interest to be paid to that account if money earns 2.4% p.a. compounding monthly.

Use the compound interest formula to show that the time it takes for an investment to double in value does not depend on the principal P, but rather depends only on the APR and the number of compoundings per year.  Let n = 12, and find the doubling rate for the following interest rates:a)  3%b)  5%c)  8%

$ Face value (principal) 52,200 Rate of interest TABLE Day of month 12% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 7-1 31 Jan. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Exact days-in-a-year calendar (excluding leap year)" 28 Feb. Length of note 95 days 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 "Ohen referred to as a Julian calendar. 56 57 58 59 31 Mar. 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 30 Apr. Maturity value 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 31 30 May June 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 30 31 31 31 July Aug. Sept. Oct. Date of note…

Compute the simple interest INT for the specified length of time and the future value FV at the end of that time (in dollars). Round all answers to the nearest cent. $7,000 is invested for 1 year at 3% per year. INT = $ FV = $