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3 years ago

$500 is invested at 6%annual interest, compounded quarterly. When will the balance double?

Mathematics

1 answer:

Setler [38]3 years ago

6 0

Answer: 48 quarters or 12 years

Step-by-step explanation:

You can use the Rule of 72 to estimate the amount of time it will take for an investment to double.

It works by dividing 72 by the interest rate per period.

The rate here is 6% but this is an annual rate yet the interest is to be compounded quarterly. You need to convert this annual rate to a quarterly rate:

= 6% / 4

= 1.5% per quarter

The amount of time it will take to double is:

= 72 / 1.5

= 48 quarters

In years that would be:

= 48 / 4

= 12 years

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a) $654.16-2.01\frac{164.55}{\sqrt{52}}=608.29$

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Part a

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Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,51)".And we see that $t_{\alpha/2}=2.01$

Replacing we got:

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$n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189$

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