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almond37 [142]
1 year ago
12

How much interest would $1,000 earn in 1 year at an annual rate of 2% compounded annually

Mathematics
1 answer:
NNADVOKAT [17]1 year ago
6 0

The Compound Interest would be $1104.895

What is Compound Interest ?

The interest charged on a loan or deposit is known as compound interest. It is the idea that we use the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The main distinction between compound and simple interest is this. If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even though the principal remains the same, the interest changes annually. We can observe that interest rises over time. As a result, we can infer that the interest the bank charges is compound interest, or CI, rather than simple interest.

Number of quarters in 5years =5×4=20

Quarterly rate of compound interest

r=24=0.5%

Initial amount

P=$1000

hence the total amount after 5years

=  P(1+r/100)n

=1000(1+0.5/100)^20

=1000(1.005)^20

=$1104.895

Hence, The Interest will be $1104.895

To learn more about Compound interest click on the link

brainly.com/question/24924853

#SPJ10

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The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep
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Ooh, fun

geometric sequences can be represented as
a_n=a(r)^{n-1}
so the first 3 terms are
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and their product is -1/125
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from the 2nd equation we can take the cube root of both sides to get
\frac{-1}{5}=ar
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r
subsituting -1/5 for ar
\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r
which simplifies to
\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for ax^2+bx+c=0
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}
so
for 2r²-5r+2=0
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b=-5
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r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}
r=\frac{5 \pm \sqrt{25-16}}{4}
r=\frac{5 \pm \sqrt{9}}{4}
r=\frac{5 \pm 3}{4}
so
r=\frac{5+3}{4}=\frac{8}{4}=2 or r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}

use them to solve for the value of a
\frac{-1}{5}=ar
\frac{-1}{5r}=a
try for r=2 and 1/2
a=\frac{-1}{10} or a=\frac{-2}{5}


test each
for a=-1/10 and r=2
a+ar+ar²=\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}
it works

for a=-2/5 and r=1/2
a+ar+ar²=\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}
it works


both have the same terms but one is simplified

the 3 numbers are \frac{-2}{5}, \frac{-1}{5}, and \frac{-1}{10}
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