Geometric Series and finance combo Critical Math.

Question

(a) A geometric series has first term a and common ratio r. Prove that the sum of the first n terms of the series is: a(1-rⁿ)/(1-r).

Mr. King will be paid a salary of £35 000 in the year 2005. Mr. King’s contract promises a 4% increase in salary every year, the first increase being given in 2006, so that his annual salaries form a geometric sequence.

(b) Find, to the nearest £100, Mr. King’s salary in the year 2008

Mr. King will receive a salary each year from 2005 until he retires at the end of 2024

(c) Find, to the nearest £1000, the total amount of salary he will receive in the period from 2005 until he retires at the end of 2024.

(d) Mr. King has a savings scheme for 2 years following his retirement from 2025-2030, compounded semiannually at a rate of 12% on his savings between 2005-2024, given that he saved 30% of his salary between 2005-2010 and 40% of his salary between 2010-2024. Find the present value upon his retirement of the net amount at the end of this savings scheme..

Answer 1

I'm using the formula for interest. In this case int=4%.

fv=p(1.int/c)^(cn)

future value

principal

int

compound/times

yrs

fv=35000(1+.04/c)^4=£39,370.24