Question

Elwood invested $5,000 in a money market account and has been tracking its progress. He found that after 3 years, the account held $7,100 and after 8 years, the account held $10,350.

Answer 1

drop down 1 a slower rate per year

drop down 2 670

Explanation:

as in three years you get $7100

you take that and subtract it by your starting amount (5000)

7100-5000= 2100

then divide 2100 by the number of years (3)

to get your annual rate of 700$

then you take the 8 year total and subtract it from your 3 year total

10350-7100= 3250

Then divide that by 5 because that how many years it has been

to get the annual rate of 650

making the 5 year rate slower.

The to find the average rate over all 8 year you take 10350 and subtract it from your starting number 5000

10350-5000= 5350

then take 5350 and divide it by the number of years (8)

you then get you average rate of 668.75

668.75=670

Hope this helps!

Answer 2

The percent of interest is 12.3% per year

Explanation:

According to the question Elwood invested 5000 $ in market account

The market account gives the compound interest annually

let p be the interest per year then

At the end of 1st year

amount =(1+0.p) x 5000 = 1.p x 5000

similarly at the end of 2nd year

amount =(1+0.p) x(1+0.p)x 5000 =
`(1.p)^(2)` x 5000

similarly at the end of 3rd year

amount = 7100 $ =
`(1.p)^3` x 5000

⇒
`(71)/(50)` =
`(1.p)^3`

1.392 =
`(1.p)^3`

on further solving we get

1.p =
`(1.42)^(1/3)` = 1.123

thus 1.p = 1 + 0.p = 1.123

thus p = 0.123

thus the percent of interest is 12.3% per year