Question

15 Points

If you invested $600 at 3% simple interest for 2 years, how much interest do you earn? Show work and answer in complete sentences to earn full credit.




If you invest $600 at 4% compounded monthly for 2 years, how much interest you do earn? Show work and answer in complete sentences to earn full credit.




Which would you rather do?

Answer 1

Simple interest = $36

Compound interest = $48.96

It's better to invest $600 at 4% compounded monthly for 2 years as it's giving us more profit.

Explanation:

Simple interest is calculated on the principal amount of a loan. Compound interest is calculated on the sum of principal amount and accumulated interest of previous periods.

Simple interest =
`(P R T)/(100)`

Compound interest =
`P(1+(R)/(100) )^T-P`

Here, P denotes principal amount, R denotes rate of interest, T denotes time.

Given: $600 invested at 3% simple interest for 2 years, $600 invested at 4% compounded monthly for 2 years

To find: Simple interest and compound interest.

Solution:

Take P=600, R=3% and T=2 years

Using the formula of simple interest mentioned above,

Simple interest =
`(600* 3* 2)/(100)=36`

So, interest earned is $36

Take P=600, R=4% and T=2 years

Using the formula of compound interest mentioned above,

Compound interest =
`600\left ( 1+(4)/(100) \right )^2-600`

=
`600\left ( 1+(1)/(25) \right )^2-600`

=
`600\left [ \left ( (26)/(25) \right )^2-1 \right ]`

=
`600\left ( (676)/(625)-1 \right )`

=
`600* (51)/(625)=48.96`

So, interest earned is $48.96

It's better to invest $600 at 4% compounded monthly for 2 years as it's giving us more profit.