Question 2A life assurance company issues a 20-year term, insurancepolicy to a life aged 40, with sum insured £100,000 payable immediately on death.Level premiums are payable monthly in advance throughout the term. Thecommissions are 10% of each premium payment (incurred at the premium paymenttimes). Mortality follows AM92 ultimate life table with uniform distribution ofdeaths (UDD) assumption between integer years. Interest is i = 6% per annum.(a) Write down an expression for the gross loss at issue random variable.(b) Write down the equation of value for this policy.(c) Calculate the gross monthly premium.

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Answered: Question 2 A life assurance company…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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On the basis of how long he has until retirement and his comfort with investment risk, Connor has decided that he wants to allocate the money in his retirement account as follows: 70% to equities, 15% to fixed income, and 15% to cash. If Connor assumes that each asset class provides the low end of the rates of return shown in the table below, what overall rate of return would he expect to earn over the long term? Asset Class Degree of Risk Historical Average Rate of Return Equities High 8% - 12% Fixed Income Moderate 4% - 7% Cash Minimal 2% - 5% Group of answer choices 4.34% 6.50% 1.43% 7.25%
You wish to retire at age 50 and receive annual birthday payments of $40,000 beginning on your 50th birthday and continuing forever (with payments going to your heirs after your death). To this end, you save in an account earning a 4% annual effective interest rate. How much money will you need to have saved by age 50, at the instant prior to your 50th birthday payment?
Table 1: Accumulated Interest Year 1 Lower-Risk Customer Higher-Risk Customer ACCUMULATED INTEREST Figure 1: Accumulated Interest 14,000.00 12,000.00 10,000.00 8,000.00 6,000.00 4,000.00 2,000.00 0 1 1,396.55 2,605.48 2 3,190.68 3,190.68 6,096.38 8,628.07 10,668.88 1,396.55 Accumulated Interest 2 6,096.38 Ⓒ2,605.48 3 Lower-Risk Customer 3,602.39 4,359.66 4,846.10 3 8,628.07 4 3,602.39 YEAR Ⓒ10,668.88 Ⓒ4,359.66 Higher-Risk Customer 5 Ⓒ12,065.44 5 Ⓒ4,846.10 12,065.44 12,616.45 5,026.46 6 6 Ⓒ12,616.45 5,026.46 4) Using the graph in 3), calculate the difference in the accumulated interest amount earned in year 5 by the credit card company charging 27.5 % versus 12.3% nominal annual rate of interest. 7
You are chairperson of the investment fund for the Continental Soccer League. You are asked to set up a fund of semiannual payments to be compounded semiannually to accumulate a sum of $210,000 after eight years at a 10 percent annual rate (16 payments). The first payment into the fund is to take place six months from today, and the last payment is to take place at the end of the eighth year. Use Appendix A and Appendix C for an approximate answer, but calculate your final answer using the formula and financial calculator methods. a. Determine how much the semiannual payment should be. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Semi-annual payment On the day after the sixth payment is made (the beginning of the fourth year), the interest rate goes up to an annual rate of 12 percent. This new rate applies to the funds that have been accumulated as well as all future payments into the fund. Interest is to be compounded semiannually on all…
Calculate the periodic rate of interest and total number of periods in each case: 12% p.a. compounded monthly for 38 months. 5% p.a. compounded quarterly for 30 months. 8% p.a. compounded semi-annually for 2 years and 8 months. 5% p.a. compounded daily for 2 years and 10 months and 12 days.
Given: 6 = 0.08; Mortality is uniformly distributed throughout life (DeMoivre) 7th w = 100. Find the APV of a continuous 10-year certain and life annuity to (50). a. 11.43 b. 12.06 c. 9.92 d. 10.03 e. 10.99
Kier Company issued $740,000 in bonds on January 1, Year 1. The bonds were issued at face value and carried a 3-year term to maturity. They had a 5.50% stated rate of interest that was payable in cash on December 31st. Based on this information alone, the amount of interest expense shown on the December 31, Year 1 income statement and the cash flow from operating activities shown on the December 31, Year 1 statement of cash flows would be: Interest Expense Cash Outflow A. $40,700 zero B. zero $40,700 C. $40,700 $40,700 D. zero zero Multiple Choice Choice A Choice B Choice C Choice D
Determine the final account balance of an investment if $300 is invested at an intrest rate of 6.75% compounded semiannually for 20 years.
a) Find the amount P that needs to be invested at a rate of 5% compounded quarterly for 6 years to give a final amount of $2000.

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