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) \(\displaystyle{4.7}\%\).

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) \(\displaystyle{4.7}\%\).