Question 346581
in 5 years you have 7800
in 9 years you have 8840
from the 5th year to the 9th year you have gained 1040.
since this is simple interest, then you have gained 1040 / 4 = 260 per year.
this can be seen as follows:
year 5 = 7800
year 6 = 8060
year 7 = 8320
year 8 = 8580
year 9 = 8840


since this is simple interest, then you gain the same interest per year and so you can work back from 7800 to get how much you started with.


since it took 5 years to get 7800, then subtract 5 * 260 from 7800 to get the principal amount in year 0.


since 5 * 260 = 1300, that would be equal to 7800 - 1300 = 6500.


your principal amount is equal to 6500.


your interest rate based on the principal amount would be equal to 260 / 6500 = .04 which is the same as 4% per year.


your yearly amounts come out to be:


year 0 = 6500
year 1 = 6760
year 2 = 7020
year 3 = 7280
year 4 = 7540
year 5 = 7800 ********
year 6 = 8060
year 7 = 8320
year 8 = 8580
year 9 = 8840 ********


you can graph the equation for simple interest as follows:


since this is simple interest, it would be a straight line graph.


let y = value
let x = number of years


your points are (x,y) = (5,7800) and (9,8840)


your slope is (8840 - 7800) / (9 - 5) = 1040 / 4 = 260


your straight line equation becomes:


y = 260*x + b


substitute one of the points in this equation to get the y-intercept.


8840 = 260*(9) + b


you get b = 6500.


your equation is therefore y = 260*x + 6500


graph of your equation looks like this:


{{{graph(600,600,-1,10,-1000,10000,260*x+6500,7800,8840)}}}


horizontal lines at y = 7800 and y = 8840 show you that the intersection of these lines with the equation occur at x = 5 and x = 9 respectively.


the interest rate had to be calculated over the principal amount at year 0.


easiest way to get the answer was to get the annual increase year over year which had to be the same because you are dealing with simple interest.