note: please make sure to properly format your answers. all dollar figures in the answers need to include…

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).\nryan deposits $775 in an account that pays 1.24% simple interest for four years. brian deposits $775 in an account that pays 1.24% simple interest for one year.\na. what is ryans interest after the four years?\nb. what is ryans balance after four years?\nc. how much interest did ryans account earn the first year?\nd. how much interest did ryans account earn the fourth year?\ne. what is brians interest after the first year?\nf. what is brians balance after the first year?\ng. suppose brian withdraws all of the principal and interest after the first year and deposits it into another one - year account at the same rate, what is his interest for the second year? round to the nearest cent.

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).\nryan deposits $775 in an account that pays 1.24% simple interest for four years. brian deposits $775 in an account that pays 1.24% simple interest for one year.\na. what is ryans interest after the four years?\nb. what is ryans balance after four years?\nc. how much interest did ryans account earn the first year?\nd. how much interest did ryans account earn the fourth year?\ne. what is brians interest after the first year?\nf. what is brians balance after the first year?\ng. suppose brian withdraws all of the principal and interest after the first year and deposits it into another one - year account at the same rate, what is his interest for the second year? round to the nearest cent.

Answer

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $I = Prt$, where $I$ is the interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

Step2: Convert the interest rate to decimal

The annual interest rate $r = 1.24%=0.0124$.

Step3: Calculate Ryan's interest after four years (a)

$P = 775$, $r = 0.0124$, $t = 4$. Using the formula $I=Prt$, we have $I = 775\times0.0124\times4=775\times0.0496 = 38.44$.

Step4: Calculate Ryan's balance after four years (b)

The balance $A$ is the sum of the principal $P$ and the interest $I$. So $A=P + I=775+38.44 = 813.44$.

Step5: Calculate Ryan's first - year interest (c)

$P = 775$, $r = 0.0124$, $t = 1$. Using the formula $I = Prt$, we get $I=775\times0.0124\times1 = 9.61$.

Step6: Calculate Ryan's fourth - year interest (d)

Since it is simple interest, the interest each year is the same. So the interest in the fourth year is also $I = 775\times0.0124\times1=9.61$.

Step7: Calculate Brian's interest after one year (e)

$P = 775$, $r = 0.0124$, $t = 1$. Using the formula $I = Prt$, we have $I=775\times0.0124\times1 = 9.61$.

Step8: Calculate Brian's balance after one year (f)

The balance $A$ is $A = P+I=775 + 9.61=784.61$.

Step9: Calculate Brian's second - year interest (g)

The new principal for the second - year is $P = 784.61$, $r = 0.0124$, $t = 1$. Using the formula $I = Prt$, we get $I=784.61\times0.0124\times1\approx9.73$.

Answer:

a. $$38.44$ b. $$813.44$ c. $$9.61$ d. $$9.61$ e. $$9.61$ f. $$784.61$ g. $$9.73$