Question 1133490
you didn't specify whether it was compound interest or simple interest.


if it was compound interest, the formula is f = p * (1 + r) ^ n


n = time period 3 minus time period 0 = 3
f = 172
p = 100


formula becomes 172 = 100 * (1 + r) ^ 3


divide both sides of the equation by 100 and take the third root of both sides of the equation to get:


(172/100) ^ (1/3) = 1 + r


solve for r to get r = (172/100) ^ (1/3) - 1.


this makes r = .198145283.


that's the interest rate per time period.


f = 100 * (1.198145283) ^ 3 becomes f = 172.


the interest rate per time period is good.


time period 10 minus time period 5 = 5


100 invested in time period 5 at the same rate for 5 time periods makes the formula equal to:


f = 100 * (1.198145283) ^ 5 which makes f equal to 246.9149645.


the accumulated value at time period 10 is 246.9149645.


the formula for simple interest 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 period.


the future value of the investment is f = p + i.
since i = p * r * n, you get f = p + p * r * n.
you can factor out the p to get f = p * (1 + r * n)


when p = 100 and f = 172 and n = 3, the formula becomes:


172 = 100 * (1 + r * 3)


divide both sides of the equation by 100 and subtract 1 from both sides of the equation and then divide both sides of the equation by 3 to get:


(172/100 - 1) / 3 = r


solve for r to get r = .24


the simple interest rate is .24 per time period.


the original equation for f is f = p + p * r * n
that becomes f = 100 + 100 * .24 * 3 which becomes f = 172.


when n = 5, the formula becomes f = 100 + 100 * .24 * 5 which becomes f = 220.


with compound interest formula, the interest rate per time period is .198145283.
in 3 years, 100 grows to 172.
in 5 years, 100 grows to 246.9149645.


with simple interest formula, the interest rate per time period is .24.
in 3 years, 100 grows to 172.
in 5 years, 100 grows to 220.


compound interest formula graph is shown below followed by simple interest formula graph.


equation for compound interest graph is y = 100 * 1.198145283 ^ x


equation for simple interest graph is y = 100 + 100 * .24 * x


here's the graphs.


<img src = "http://theo.x10hosting.com/2019/012701.jpg" alt="$$$" >


<img src = "http://theo.x10hosting.com/2019/012702.jpg" alt="$$$" >