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Sergio [31]
1 year ago
6

Explain the error a student is asked to find when the value of an investment of $5200 is an account that earns 4.2% annual inter

est compounded quarterly reaches $16,500. The student uses the model V(t)=5200(1.014)^3t and finds that the investment reaches a value of $16,500 after approximately 27.7 years. Fine and correct the students error.
Mathematics
1 answer:
zloy xaker [14]1 year ago
5 0

We are given the following information

Investment = $5200

Annual interest rate = 4.2% = 0.042

Final amount = $16,500

Number of years = 27.7 years

Number of compoudings = quartely = 4

The student uses the following model

V(t)=5200(1.014)^{3t}

The general formula for compound interest is given by

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

As you can see, the number of compoundings is incorrect (3 vs 4)

The interest rate is also incorrect.

Let us substitute the given values into the above formula

\begin{gathered} V(t)=P(1+\frac{r}{n})^{nt} \\ V(t)=5200(1+\frac{0.042}{4})^{4\cdot27.7} \\ V(t)=5200(1+0.0105)^{110.8} \\ V(t)=5200(1.0105)^{110.8} \\ V(t)=\$16543.5^{} \end{gathered}

Therefore, the final amount is approximately $16,543.5

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Here are two ways of doing it.

************************************************************

1) The current price is 100% of the price. The price went down by 6%, so since 100% - 6% = 94%, the new price is 94% of the original price.

94% * 175 = 0.94 * 175 = 164.50

The new price is 164.50

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2) The discount is 6% of 175, so first, we find the discount.

6% of 175 = 0.06 * 175 = 10.5

Now we subtract the amount of the discount from the original price.

175 - 10.50 = 164.50

The new price is 164.50

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As you can see, both methods give you the same answer, 164.50
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Explanation:

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Insert the values in the above formula:

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or, F(3) = 4×(1/27)

therefore, F(3)= 4/27... ans

<em><u>hope</u></em><em><u> </u></em><em><u>it helps</u></em><em><u>.</u></em><em><u>.</u></em>

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