Question 1121607
with simple interest, the formula used is:


i = p * r * n


i is the interest
p is the principal
r is the interest rate per time period
n is the number of time periods


also:


f = p + i


f is the future value
p is the principal
i is the interest


in your problem.


r = 40% per year = .4 per year = .4/12 per month


n = 6 months


formula for i says i = p * r * n which becomes i = p * .4 / 12 * 6 which becomes i = p * .2.


f = p + i becomes f = p + p * .2.


since f = 840, this formula becomes 840 = p + p * .2 which becomes 840 = p * (1 + .2) which becomes 840 = p * 1.2.


divide both sides by 1.2 to get 840 / 1.2 = p = 700.


the principal amount is 700.


using p = 700 and r = .4/12 and n = 6, you get i = 700 * .4/12 * 6 = 140


f = p + i becomes f = 700 + 140 = 840.


numbers check out.


solution is that the amount invested is 700.