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Question 1152584: Arnold invest $250 four years ago. Investment is now worth $320 due to a simple interest earned. How much did Arnold earn in interest per year and what was the simple interest rate?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the investment is 250 4 years ago.
investment is now worth 320.
simple interest formula is i = p * r * n
i = interest earned
p = principal
r = interest rate per time period
n = number of time periods.
interest earned is the future value minus the amount invested.
this is equal to 320 - 250 = 70
n = 4 years
formula becomes:
70 = 250 * r * 4
solve for r to get:
r = 70 / (250 * 4) = .07
the interest rate per year is 7%.
250 earns 7% per year for 4 years.
you get 250 * .07 * 4 = 70
add that to the 250 and the investment is now worth 320.
simple interest is only earned on the initial investment.
if you want to earn interest on the interest previously earned, then you are getting into a compound interest formula.
the formula for that is:
f = p * (1 + r) ^ n
f = future value
p = present value
r = interest rate per time period
n = number of time period.
with this formula, the interest rate will be less because you're earning interest on the previous interest earned.
for example:
320 = 250 * (1 + r) ^ 4
subtract 250 from both sides of this equation to get:
320 / 250 = (1 + r) ^ 4
take the fourth root of both sides of the equation to get:
(320 / 250) ^ (1/4) = 1 + r
solve for r to get:
r = (320 / 250) ^ (1/4) - 1 = .0636591794 = 6.37% approximately.
with simple interest, you get 7% per year.
with compound interest, you get 6.37% per year.
if the compound interest rate was 7% per year, you would have more than 320 in the account after 4 years.
i'd go with 7% per year since i think that's what they're looking for.
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