Step 1

a) Simple interest for an amount P, at an interest rate of r (in decimals) per annum and for T years is given by:

Plugging the values:

\(\displaystyle{I}={P}{T}{r}\)

\(\displaystyle{I}={\left({10000}\right)}{\left({4}\right)}{\left({0.055}\right)}\)

\(\displaystyle{I}={2200}\)

Step 2

b) Amount after continuous compounding for T years of principle P at an interest rate of r is given by:

Plugging the values:

So the interest is given by:

\(\displaystyle{A}={P}{e}^{{{r}{T}}}\)

\(\displaystyle{A}={\left({10000}\right)}{e}^{{{\left({0.05}\right)}{\left({4}\right)}}}\)

\(\displaystyle{A}={\left({10000}\right)}{e}^{{{0.2}}}\)

\(\displaystyle{A}={\left({10000}\right)}{\left({1.221402}\right)}\)

\(\displaystyle{A}={12214.03}\)

\(\displaystyle{I}={12214.03}-{10000}={2214.03}\)

Step 3

c) Hence, simple interest results in less total interest.

a) Simple interest for an amount P, at an interest rate of r (in decimals) per annum and for T years is given by:

Plugging the values:

\(\displaystyle{I}={P}{T}{r}\)

\(\displaystyle{I}={\left({10000}\right)}{\left({4}\right)}{\left({0.055}\right)}\)

\(\displaystyle{I}={2200}\)

Step 2

b) Amount after continuous compounding for T years of principle P at an interest rate of r is given by:

Plugging the values:

So the interest is given by:

\(\displaystyle{A}={P}{e}^{{{r}{T}}}\)

\(\displaystyle{A}={\left({10000}\right)}{e}^{{{\left({0.05}\right)}{\left({4}\right)}}}\)

\(\displaystyle{A}={\left({10000}\right)}{e}^{{{0.2}}}\)

\(\displaystyle{A}={\left({10000}\right)}{\left({1.221402}\right)}\)

\(\displaystyle{A}={12214.03}\)

\(\displaystyle{I}={12214.03}-{10000}={2214.03}\)

Step 3

c) Hence, simple interest results in less total interest.