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AlekseyPX
3 years ago
11

You deposit $200 in an account earning 3% interest compounded

Mathematics
1 answer:
anastassius [24]3 years ago
5 0

Answer:

$268.78

Step-by-step explanation:

We will use the compound interest formula to solve this:

A=P(1+\frac{r}{n} )^{nt}

<em>P = initial balance</em>

<em>r = interest rate (decimal)</em>

<em>n = number of times compounded annually</em>

<em>t = time</em>

First, change 3% into its decimal form:

3% -> \frac{3}{100} -> 0.03

Now, plug in the values:

A=200(1+\frac{0.03}{1})^{1(10)}

A=268.78

After 10 years, you will have $268.78

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Find the sum of a finite geometric sequence from n = 1 to n = 7, using the expression −4(6)n − 1.
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Answer:

<h2>-223,948</h2>

Step-by-step explanation:

The formula of a sum of terms of a gometric sequence:

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We have

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Calculate a₁. Put n = 1:

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r=\dfrac{a_{n+1}}{a_n}\\\\a_{n+1}=-4(6)^{n+1-1}=-4(6)^n\\\\r=\dfrac{-4(6)^n}{-4(6)^{n-1}}=6^n:6^{n-1}\\\\\text{use}\ a^n:a^m=a^{n-m}\\\\r=6^{n-(n-1)}=6^{n-n+1}=6^1=6

\text{Substitute}\ a_1=-4,\ n=7,\ r=6:\\\\S_7=-4\cdot\dfrac{1-6^7}{1-6}=-4\cdot\dfrac{1-279936}{-5}=-4\cdot\dfrac{-279935}{-5}=(-4)(55987)\\\\S_7=-223948

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