# The closed nominal annual rate of return. Given: Initial Cost is $1000. Future cost is$2500. Interest is compounded quarterly. The time period is 5 years.

The closed nominal annual rate of return.
Given: Initial Cost is $1000. Future cost is$2500.
Interest is compounded quarterly.
The time period is 5 years.

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Calculation:
Write the expression to calculate the future value.
$$\displaystyle{F}={P}{\left({1}+{i}\right)}^{{{n}}}$$ .......(I)
Here, the future value is F, the present value is P, the rate of interest is i and the time period is n.
Substitute $1000 for P,$2500 for F and 20 for n in Equation (I).
$$\displaystyle\{2500}=\{1000}{\left({1}+{i}\right)}^{{{20}}}$$
$$\displaystyle{i}={\left({2.5}\right)}^{{{\frac{{{1}}}{{{20}}}}-{1}}}$$
$$\displaystyle{i}={0.0468}\times{100}\%$$
$$\displaystyle{i}\approx{4.7}\%$$
Conclusion:
Thus, the correct answer is option (b) $$\displaystyle{4.7}\%$$.