SOLUTION: At a particular rate of simple interest, $1200 invested at time t=0 will accumulate to $1300 in T years. find the accumulated value of $500 invested at the same rate of simple inte

Question 1000333: At a particular rate of simple interest, $1200 invested at time t=0 will accumulate to $1300 in T years. find the accumulated value of $500 invested at the same rate of simple interest and again at t=0, but this time 2T years
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
With simple interest
I=prt
100=1200*r*t
rt=(1/12)
r*2t=(1/6), which is the "new" rt for the second part
I=prt; I=500*(1/6)=$83.33
Accumulated value=$583.33
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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

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