Question 1000333
i = p * r * n
f = p + i


i = interest
p = present value of investment.
r = interest rate per time period
n = number of time periods
f = future value of investment


you are given that you invested 1200 and you had 1300 after T years.
your interest is therefore equal to 100 because 1300 - 1200 = 100
your interest rate is 100 / 1200 = 1/12 per time period
your time period is T years.
n is the number of time periods = 1.


applying the fomula to what you were given results in:


i = p * r * n, which becomes:


100 = 1200 * 1/12 * 1


since this gets you 100 = 100, the values given for the variables involved are good.


in the second part of your problem, you are given that  your initial investment is 500 and that it is invested at the same rate as in the first part of your problem, but for 2T years.


p = 500
r = 1/12 per time period.
n = 2 time periods.


you solve for i to get:


i = 500 * 1/12 * 2 = 500 * 2/12 = 83.33


f = p + i becomes f = 500 + 83.33 = 583.33