3. (AMLCR) 6.16.A life insurance company sells annuities to men aged exactly 60. Each policyholder pays asingle net premium, P, and then receives an annuity of $30,000 a year in arrear (so that thefirst annuity payment is on the 61st birthday). Assume that mortality follows the StandardSelect Life Table, and that the interest rate is 5% per year.(a) Calculate P.(b) Calculate the probability that the present value of profit on a single policy is positive.(c) Calculate the standard deviation of the present value of profit on a single policy.(d) Now suppose that the office sells 1,000 such annuities simultaneously to independentlives. Calculate the value of P such that the probability that the present value of the profitto the insurance company is positive is 95%.

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Answered: A life insurance company sells…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Stocks A and B have the following historical returns: Year 2016 2017 2018 2019 2020 a. Calculate the average rate of return for each stock during the period 2016 through 2020. Round your answers to two decimal places. Stock A: % % Stock A's Returns, ra (20.60%) 39.75 17.25 (3.50) 25.00 Stock B: b. Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been each year? Round your answers to two decimal places. Negative values should be indicated by a minus sign. CV Stock A Stock B's Returns, B (14.30%) 29.80 37.30 (6.60) 11.70 Year 2016 2017 2018 2019 2020 What would the average return on the portfolio have been during this period? Round your answer to two decimal places. Portfolio % c. Calculate the standard deviation of returns for each stock and for the portfolio. Round your answers to two decimal places. Stock B % Portfolio % Stock A % Standard Deviation d. Calculate the coefficient of…
The annuity will run out of funds after approximately 13 years 10 months. (b) Show that a continuous annuity with withdrawal rate N = $5000/year and interest rate r = 8%, funded by an initial deposit of P0 = $75,000, never runs out of money.
Emma wants to donate $1,000,000 to establish a fund to provide an annual scholarship in perpetuity. The fund will earn an interest rate of j4=2.47% p.a. effective and the first scholarship will be first awarded 2.5 years after the date of the donation. (b) Assume that the fund's earnings rate rate has changed from j4=2.47% to j4=2.22% one year before the first scholarship payment. How much does Emma need to add to the fund at that time (one year before the first scholarship payment) to ensure that scholarship amount will be unchanged (rounded to two decimal places)? a. 120871.62 b. 117931.61 c. 116810.57 d. 113655.15
A 10-year annuity makes continuous payments. At time tt, the annuity pays at an annual rate of (30−3t)(30−3t). Time is measured in years. At an annual effective interest rate of 5%, calculate the present value of the annuity. A. 128.31 B. 140.18 C. 144.51 D. 156.00 E. 201.03
An investment opportunity promises to pay off an amount of P1,000,000 seven years from now if one invests P400,000 today. If the interest is compounded in a semi-annual basis, what is the assumed interest rate for the investment?
Illu.16 : On 31st Lecember, 2003 Andhra Traders Lid, shored in thei accouts the following balances : Rs. 1.50.000 Debenture Redemption Fund Debenture Redemption Fund Investments 1.50,000 5% Debentures 150,000 On 1st March, 2004, the Company sold the investments for Rs.150,500 and the debentures were paid off. Prepare (a) Debenture A/e (b) Debenture Redemption Fud a/c (c) Debenture Redemption Fund Investment a/e. CS Scanned with CamScanner

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