An insurer is designing a 10-year single premium variable annuity policy with a guaranteed maturity benefit of 85% of the single premium. (a) Calculate the value of the GMMB at the issue date for a single premium of $100. (b) Calculate the value of the GMMB two years after issue, assuming that the policy is still in force, and that the underlying stock prices have decreased by 5% since inception. Basis and policy information: Age at issue: 60 Front end expense loading: 2% Annual management charge: 2% at each year end (including the first) Survival model: Standard Ultimate Survival Model Lapses: 5% at each year end except the final year Risk-free rate: 4% per year, continuously compounded Volatility: 20% per year

An insurer is designing a 10-year single premium variable annuity policy with a guaranteed maturity benefit of 85% of the single premium. (a) Calculate the value of the GMMB at the issue date for a single premium of $100. (b) Calculate the value of the GMMB two years after issue, assuming that the policy is still in force, and that the underlying stock prices have decreased by 5% since inception. Basis and policy information: Age at issue: 60 Front end expense loading: 2% Annual management charge: 2% at each year end (including the first) Survival model: Standard Ultimate Survival Model Lapses: 5% at each year end except the final year Risk-free rate: 4% per year, continuously compounded Volatility: 20% per year

EBK CONTEMPORARY FINANCIAL MANAGEMENT

14th Edition

ISBN:9781337514835

Author:MOYER

Publisher:MOYER

Chapter5: The Time Value Of Money

Section: Chapter Questions

Problem 44P

See similar textbooks

Similar questions

The annual payment of a 10-year fixed-income security is $50. The payments are made at the end of each year. The market-required rate of return is 10%. What is the current price of the securities?
Assume that as of today, the annualized interest rate on a three-year security is 3 percent, while the annualized interest rate on a two-year security is 2.15 percent. Use this information to estimate the one-year forward rate two years from now.
A senior executive is offered a buyout package by his company that will pay him a monthly benefit for the next 20 years. Monthly benefits will remain constant within each of the 20 years. At the end of each 12− month period, the monthly benefits will be adjusted upwards to reflect the percentage increase in the CPI(an inflation rate). You are given:
Your client is invested in a registered indexed-linked annuity (RILA). The RILA contains a 7% floor, an 80% participation rate, and an overall cap rate of 10%. Suppose in years one and two, the S&P 500 returns 12% and -10%, respectively. What interest rate would be credited to the RILA during these two years? A) Year 1: 10% / Year 2: -7% B) Year 1: 9.6% / Year 2: -7% C) Year 1: 9.6% / Year 2: -3% D) Year 1: 9.6% / Year 2: -10%
An insurance company sells an annuity that provides 20 annual payments, with the first payment beginning one year from today and each subsequent payment 2% greater than the previous payment. Using an annual effective interest rate of 3%, the present value of the annuity is 200,000. Calculate the amount of the final payment from this annuity.......
An insurance company offers a retirement annuity that pays 100,000 per year for 15 years, gorwing at an "inflation compensator" rate of 3%, and sells for $806,070. What is the interest rate? show your work
A pension plan is obligated to make disbursements of $1.9 million, $2.9 million, and $1.9 million at the end of each of the next three years, respectively. The annual interest rate is 11%. If the plan wants to fully fund and immunize its position, how much of its portfolio should it allocate to one - year zero - coupon bonds and perpetuities, respectively, if these are the only two assets funding the plan?
An insurer needs to make the following annuity payments to an individual: £445 paid at the end of each month during the first 15 years and then £448 paid at the end of each 4 months for the following 8 years. Assuming an effective monthly interest rate of 1.3% throughout the entire period, how much total fund the insurer needs to hold today in order to meet these payments? ( correct answer =31470.44, using formulas no tables)
What is thevpresent value of an annuity of 1,600 per year for 10 years, with the first payment occurring at the end of year 10 ( that is, ten 1,600 payments occurring at the end of year 10 through year 19), given a discount rate of 9 percent?
A pension plan must make total disbursements of $4.7 million, $6.7 million, $5.7, $3.0 and $1.0 million annually for the next five years, respectively. The fund makes these payments twice a year, paying half of each year's total amount six months into the year and the remaining half at the end of the year.Find the duration of the pension obligations if spot rates are flat at 8%. Group of answer choices 1.91 3.86 4.76 2.00 2.17
Assume the following for a one-year rate adjustable rate mortgage loan that is tied to the one- year Treasury rate and has monthly payments: Loan amount:150,000 Annual rate cap:2% Life-of-loan cap:5% Margin:2.75% First-year contract teaser rate:5.50%One-year Treasury rate at end of year 1:5.25% One-year Treasury rate at end of year 2:5.50% Loan term in years:30 years Given these assumptions, calculate the following: a) Initial monthly payment; b) Loan balance end of year 1; c) Year 2 contract rate; d) Year 2 monthly payment; e) Loan balance end of year 2;f) Year 3 contract rate; g) Year 3 payment.
Professor’s Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $81,000 at age 65, the firm will pay the retiring professor $625 a month until death. a. If the professor’s remaining life expectancy is 15 years, what is the monthly interest rate on this annuity? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) b. What is the effective annual interest rate? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. If the monthly interest rate is 0.75%, what monthly annuity payment can the firm offer to the retiring professor? (Do not round intermediate calculations. Round your answer to 2 decimal places.)