Question

Linda's salary is $43000 a year. As a part of it's incentive program the company decides to give her a raise of $2000 every year. What is the discounted value of her income for the next 11 years at j₁=6%? *do not round intermediate steps*

Answer 1

Beginning salary - 43000$

Raise - $2000 per year

Time - 11 years

Interest rate - 6%

So every year for the next eleven years her salary increases by 2000:

Considering the salary is increased by 2000, we start with 45,000 as the salary a year from now:

Year	1	2	3	4	5	6	7	8	9	10	11
Salary	45000	47000	49000	51000	53000	55000	57000	59000	61000	63000	65000

Discounting these salaries to the current date at 6% with the following formula:

Sum of ( salary / (1+ rate/100)^n )

where, n - year

First finding the discounting rates: [ 1/ ( 1+rate)^n ]

Then multiply the rates with the salary of that year.

Then sum the present values.

Year	1	2	3	4	5	6	7	8	9	10	11
Salary	45000	47000	49000	51000	53000	55000	57000	59000	61000	63000	65000
Discount rates	0.9433962	0.89	0.83962	0.792094	0.747258	0.7049605	0.6650571	0.6274124	0.5918985	0.55839	0.526788
Present Value	42452.83	41829.8	41141.3	40396.78	39604.68	38772.83	37908.255	37017.33	36105.806	35178.9	34241.19
SUM	424649.75

Thus, the value of her income for the next 11 years is 424,649.75$

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