Question

When $1,000 is invested at 5% simple interest, the amount grows by $50 each year. When money is invested at 5% interest com-pounded annually, the amount at the end of each year is 1.05 times the amount at the beginning of that year. Display the amounts after the first four years for a $1,000 investment at 5% simple and compound interest.

Answer 1

See the explantaion

Step-by-step explanation:

Simple Interest:

In simple interest, the interest at the end of each year remains the same.

If $1000 are invested at 5% simple interest. Simple interest per year is:

`(5)/(100)\cdot1000= 50`

Which means amount increases by $50 each year for simple interest.

Amount after 1 year :

$1000 + $50 = $1050

Amount after 2 years :

$1050 + $50 = $1100

Amount after 3 years :

$1110 + $50 = $1150

Amount after 4 years :

$1150 + $50 = $1200

Compound Interest:

In compound interest, the interest is added to the principle amount after each year, and the interest for next year is calculated on that principle amount + interest of previous year.

Initial Investment = $1000

Amount after 1 year :

Amount of interest =
`(5)/(100)\cdot1000=50\\`

Amount after 1 year = $1000 + $50 = $1050

Amount after 2 years :

Amount of interest =
`(5)/(100)\cdot1050=52.5\\`

Amount after 2 years = $1050 + $52.5 = $1102.5

Amount after 3 years :

Amount of interest =
`(5)/(100)\cdot1102.5=55.125\\`

Amount after 3 years = $1102.5 + $55.125 = $1157.625

Amount after 4 years :

Amount of interest =
`(5)/(100)\cdot1157.625=57.881\\`

Amount after 4 years = $1157.625 + $57.881 = $1215.506