Question

Rose and Dennis each open a savings account at the same time. Rose invests $2,600 in an account yielding 4.1% simple interest, and Dennis invests $2200 in an account yielding 5.7% simple interest. After nine years, who has the greater total amount of money, and how much greater is it?

Answer 1

Rose has greater total amount of money than Dennis by $230.8 .

Explanation:

Formula

`Simple\ interest = (Principle* Rate* Time)/(100)`

Amount = Principle + Simple interest

As given

Rose and Dennis each open a savings account at the same time.

Rose invests $2,600 in an account yielding 4.1% simple interest for 9 years .

Put all the values in the formula

`Simple\ interest = (2600* 4.1* 9)/(100)`

`Simple\ interest = (95940)/(100)`

Simple interest = $959.4

Thus

Amount = $2600 + $959.4

Amount = $ 3559.4

Thus total amount in the Rose saving account is $3559.4 .

As given

Dennis invests $2200 in an account yielding 5.7% simple interest for 9 years .

Put all the values in the formula

`Simple\ interest = (2200* 5.7* 9)/(100)`

`Simple\ interest = (112860)/(100)`

Simple interest = $1128.6

Thus

Amount = 2200 + 1128.6

Amount = $ 3328.6

Thus total amount in the Dennis saving account is $ 3328.6 .

As clearly Rose has greater amount of money as compared to Dennis .

Greater amount Rose has = Amount in the Rose saving account - Amount in the Dennis saving account .

Put values in the above

Greater amount Rose has in saving account = $3559.4 - $3328.6

= $ 230.8

Therefore the Rose has greater total amount of money than Dennis by $230.8 .

Answer 2

Simple interest is calculated by adding the principal amount with the product of the principal amount, interest rate and the the time or period.

Rose's money = P + PrtRose's money = 2600 + 2600(0.041)(9)Rose's money = $3559.4

Dennis' money = 2200 + 2200(0.057)(9)Dennis' money = $3328.6

Thus, Rose has the greater amount of money and is $230.4 greater than Dennis.