Please help me answering this question? (Uncertain annuity)?

Please help me answering this question?
(Uncertain annuity) Gavin’s grandfather, Mr. Jones, has just turned 90 years old and is applying for a lifetime annuity that will pay $10,0000 per year, starting 1 year from now, until he dies. He asks Gavin to analyze it for him. Gavin finds that according to statistical summaries, the chance (probability) that Mr. Jones will die at any particular age is as follows:

age: 90 91 92 93 94 95 96 97 98 99 10 101
probability:.07 .08 .09 .10 .10 .10 .10 .10 .10 .07 .05 .04

The Gavin (and you) answers the following questions:
(a) What is life expectancy of Mr. Jones?
(b) What is the present value of an annuity at 8% interest that has a lifetime equal to Mr. Jones’s life expectancy? (For an annuity of a nonintegral number of years, use an average method. )
(c) What is the expected present value of the annuity?

A simple question on bonds ?

Consider the example below (Please avoid too much jargon) :

Face value of a bond = $1000

(1) Issuing a bond at par –

coupon rate = market rate = 10% per year or 5% semi-annually.
present value or principal = 822.7
Interest = 177.3 (because an annuity of $50 is paid.)
TOTAL = 1000.

>>>what do i have to pay to purchase this bond ? 1000 or 822.7 ?
My textbook says that the company gets full use of the $1000, per bond.
>>>What does this mean ?

NOW THE EVEN MORE CONFUSING PART :

(2)Issuing bond at a discount –

market rate = 12 % , coupon = 10 %
present value or principal = 792.1
Interest = 173.25
TOTAL = 965.35

The textbook says that the company RECEIVES 963.35 per bond.

>>>Why not ask people to pay 1000 instead of 965.35 and offer them interest at market rate instead of these calculations ?

NOTE : This is taken form the book “Introduction to financial accounting” by horngren, sundem and eliott.
@JKRB – you said “and the discount of 36.35 makes up for the interest the buyers are losing for purchasing the 10% bonds when the market rate is 12%”.

Can you show mathematically, that the investors are losing 36.65 ? Then it would be easier to see that a lower selling price would make the interest higher.
My book presents the concept in a rather confusing way.
I was looking for some kind of mathematical proof which will show :

money lost by investor due to low coupon = discount offered.
Hence, no money lost by investor.

Can anybody explain following Actuarial problems step by step?

Can anybody explain following Actuarial problems step by step?
1.Mohan and John have equal amounts of money to invest. Mohan purchases a 10 year annuity-due with annual payments of Rs. 2500 each. John invests his money in a savings account earning 9% effective annual interest for two years. At the end of two years, he purchases a 15-year immediate annuity with annual payments of Z. If both annuities are valued using an effective annual rate of 8% find the value of Z.
(Answer-Rs.2514.75)
2.In fund X money accumulates at force of interest δt = .01t+.010 for 0

INSURANCE PLAN FOR CHILD?

HI.. I want to know which is the best insurance plan for the childrens from L.I.C OF INDIA..
Jeevan Anurag
Komal Jeevan

Educational Annuity Plan
CDA Endowment Vesting At 18

Jeevan Kishore Jeevan Chhaya
Child Career Plan Child Future Plan
Child Fortune Plus

MY child is 2 yrs old
Serious answers only if possible with explainations