Question 130158: Hi,
Not sure if this is correct, but is the answer 52,000? I am thinking that the problem should be set up as follows:
650,000 x 4% for two years...therefore 650,000x8%????
Question:
If 650,000 is invested in an account paying simple annual interest, how much interest will be earned in two years at the annual rate of 4%?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You make a little more than that.
.
You can look at the problem in two stages. The first year you have $650,000 invested at
a simple interest rate of 4% (or 0.04) which, because simple interest is used, is paid at the
end of the year. At the end of the first year you have your principal plus 4% of the principal.
So you actually have 1.04 of your principal at the end of the year. This can be calculated as:
.
($650,000)*(1.04) = $676,000
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Therefore, during the second year, you will have $676,000 invested at 4%. So similarly to
the first year you can multiply the principal times 1.04 to find your worth at the end of the
second year. So for the second year you find your worth by multiplying $676,000 by 1.04 and
you get:
.
($676,000)*(1.04) = $703,040
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Then you find the interest you made during the two years by subtracting your original
investment from your worth at the end of the second year to find that your total interest
for the two-year period is:
.
$703,040 - $650,000 = $53,040
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Another way you can look at this is that at the end of the first year your investment is
worth:
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($650,000)*(1.04)
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Then to find your worth at the end of the second year, you multiply what you have at the
end of the first year by 1.04. This means that at the end of the second year you have:
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(($650,000)*(1.04))*(1.04)
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This can be simplified to:
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($650,000)*(1.04)^2
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With a little more thought you can extend this into a formula for simple interest. Let
"P" represent your initial investment (the principal), "I" represent the annual interest rate as
a decimal, and "N" represent the number of years the principal and the interest are left to
accumulate. At the end of N years your account will contain an amount A as follows:
.
A = P*(1 + I)^N
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Just subtract P (original investment) from A (amount after N years) and you will have the interest
that you have made during the N years.
.
Hope this helps you to understand the problem.
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