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Nataly_w [17]
2 years ago
11

If $500 were to compound

Mathematics
2 answers:
marysya [2.9K]2 years ago
8 0

Answer:

$850

Step-by-step explanation:

Interest = original amount x rate (as a decimal) x time (in years)

I = 500 x 0.07 x 10

I = 350

Sinc the interest is 350, we add that to the original amount of 500 to find the total amount after 10 years.

500 + 350 = 850

I hope this helped and please mark me as brainliest!

GrogVix [38]2 years ago
8 0

Answer:

Total amount: $1,006.88

Step-by-step explanation:

Given the principal amount of $500 that is compounded continuously for 10 years at an annual interest rate of 7%:

We can use the following <u>Continuous Compound Interest Formula</u> to determine the future value of the total amount of investment:

\displaystyle\mathsf{\Bigg\ Continuous\:Compound\:Interest:\quad\ A\:=\:Pe^{(r\times\\ t)}}

where:

<em>A</em><em> </em>= The future value of the total amount in the account at the end of "t" number of years

<em>P</em> = Present value of the principal amount invested = $500

<em>e</em> = constant (base of the exponential function) ≈ 2.71828

<em>r</em> = Annual interest rate = 7% or 0.07

<em>t</em> = time (in years)  = 10 years

<h2 /><h2>Solution:</h2>

Substitute the given values into the  <u>Continuous Compound Interest Formula</u>:

\displaystyle\mathsf{\Bigg\ Continuous\:Compound\:Interest:\quad\ A\:=\:Pe^{(r\times\\ t)}}

\displaystyle\mathsf{A\:=\:$500\:\times\ 2.71828 ^{(0.07\times\\ 10)}}

\displaystyle\mathsf{A\:=\:$500\:\times\ [2.71828 ^{(0.70)}]}

\displaystyle\mathsf{A\:=\:$500\:\times\ 2.013752707}

\displaystyle\mathsf{A\:=\$1,006.88}}  

Therefore, the total amount accumulated after continuously compounding the principal investment for 10 years is $1,006.88. This includes the principal amount invested, $500, plus the interest accrued of $506.88.  

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