Question

if your starting salary were $50,000 and you received a 4% increase at the end of every year for 15 years, what would be the total amount in dollars you would have earned over the 16 years that you worked?

Answer 1

SO 15 or 16 years?

Answer 2

16

Answer 3

50,000 let's find what 1 percent of that is: divide by 100
1% = 50,000 /100 = $500

Answer 4

Now, if we want to find 4% , then we simply multiply 1% (or $500) by 4 to give us:
$2,000.

Answer 5

So, at the end of the first year you would have S57,000.
but there is a much easier way to do this:
F= P(1 + i)^n
this is the formula for the future value

Answer 6

I know the sequence would be.
a_N = 50000(1.04)^n-1
but it says it ends after 15 years so i'm a bit confused at that part

Answer 7

so the 4% yearly increase ends at 15 years, and so the salary that would be paid out at the end of the 16th year would be the same salary that was paid out at the end of the 15th year.

Answer 8

okay so ,
the 15th year is
a_N = 50000(1.04)^n-1
for the 15th year..
n = 16.
a_16 = 50000 (1.04)^15
a_ 16 = 90047 dollars
but then its a sum of all of them.

Answer 9

a_N = 50000(1.04)^15-1
=90046.17
is the amount at the end of year 15 that will be paid to him at that year.
since his his increase stops after year 15, then his salary at the end of year 16 will also be 90046.17

to get the total amount of money made for all the years,
take the integral of your function:
= 50000(1.04)^n-1 and evaluate it from n=0 to n=15, then add the value of 90046.17 to make up for the 16th year