Question

Answer:7. Which of the following accounts, if any, will return the greatest interest?Answer:a. 5.0% simple interestc. 5.0% interest compounded monthlyb. 5.0% interest compounded quarterly d. All of these return the same amount of interest.

Answer 1

We need to find the greatest interest in given options.

Let the principal amount be, P= $100.

The number of years, t =1

Consider the individual options.

a)

Simple interest,r = 5.0 % =0.05.

Consider the formula to find the simple interest.

`SI=Prt`

Substitute P=100, r =0.05 and t=1 in the equation.

`SI=100*0.05*1`

`SI=\text{ \$}5`

b).

Compound interest, r =5.0% =0.05.

n=4.

Consider the formula to find the compound interest.

`CI=P(1+(r)/(n))^(nt)-P`

Substitute n=4, P=100, r =0.05 and t=1 in the equation.

`CI=100(1+(0.05)/(4))^(4*1)-100`

`CI=\text{ \$}5.094`

c).

Compound interest, r =5.0% =0.05.

n=12.

Consider the formula to find the compound interest.

`CI=P(1+(r)/(n))^(nt)-P`

Substitute n=12, P=100, r =0.05 and t=1 in the equation.

`CI_1=100(1+(0.05)/(12))^(12*1)-100`
`CI_1=\text{ \$}5.116`

We know that

`5.116>5.094>5`
`CI_1>CI>SI`

5.0% interest compounded monthly will return the greatest interest.

Final answer:

5.0% interest compounded monthly