8. If $1,000 is invested in an account that pays 3% interest compounded annually, an expression that represents the amount in the account at the end of two years can be given by which of the following equations?
1000(0.3)^2
1000 +0.2^3
1000(1.03)^2
1000(0.3)^2
1000 +0.2^3
1000(1.03)^2
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1000(1.03)^2
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The answer to this question is 1000(1.03)^2.
The first answer is wrong because 3% is .03 when converted to decimal; .3 would be 30%
The second answer is wrong because it does not follow the exponential model that interest usually follows.
Most importantly, the third answer choice is right because each year, the 1000 dollars gains 3 percent interest.
The least equation expresses this, as 1000 * 1.03^2 = 1000 * 1.03 * 1.03
Reading the expression from left to right, you get that the 1000 dollars is getting an increase of 3%
(being multiplied by 1.03)
and, one year later, that (1000 dollars + the three percent interest) is gaining 3% of itself.
For reference the yearly compound interest formula follows this:
Final Amt. = Starting amount * (1 + rate)^(number of years)
The first answer is wrong because 3% is .03 when converted to decimal; .3 would be 30%
The second answer is wrong because it does not follow the exponential model that interest usually follows.
Most importantly, the third answer choice is right because each year, the 1000 dollars gains 3 percent interest.
The least equation expresses this, as 1000 * 1.03^2 = 1000 * 1.03 * 1.03
Reading the expression from left to right, you get that the 1000 dollars is getting an increase of 3%
(being multiplied by 1.03)
and, one year later, that (1000 dollars + the three percent interest) is gaining 3% of itself.
For reference the yearly compound interest formula follows this:
Final Amt. = Starting amount * (1 + rate)^(number of years)
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The formula for simple compound interest is
Principal(1+APR)^years
So, in this case, the answer can be found using 1000(1.03)^2
Principal(1+APR)^years
So, in this case, the answer can be found using 1000(1.03)^2
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compound annually P = Po (1 + r) ^t
= 1000 (1.03)^2
= 1000 (1.03)^2