Question

You deposit $450 into an account that earns simple interest at a rate of 8% APR. Your cousin deposits $450 into an account that has the same interest rate, but the interest is compounded annually. a. Calculate how much money you will have in your account at the end of 5 years. SHOW ALL YOUR WORK ON PAPER. Your ending balance: b. Calculate how much money your cousin will have in your account at the end of 5 years. SHOW ALL YOUR WORK ON PAPER. Your cousin's ending balance:

Answer 1

Given:

a statement is given about the simple interest and compound interest as following

"You deposit $450 into an account that earns simple interest at a rate of 8% APR. Your cousin deposits $450 into an account that has the same interest rate, but the interest is compounded annually"

Find:

we have to answer part (a) and part(b) as asked in the question.

Step-by-step explanation:

part(a):

Principal (P) = $450

interest rate R = 8%

Time(t) = 5 years

Therefore, Simple interest is

`S.I.=(P* R* t)/(100)=(450*8*5)/(100)=180`

Therefore amount after 5 year = Principal + Simple interest

= $450 + $180

= $630

Ending Balance = $630

part(b):

Principal (P) = $450

interest rate R = 8% (Compounded annually)

interest in decimal r = 8/100 = 0.08 rate per year

Time(t) = 5 years

Amount after 5 year is

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=450(1+(0.08)/(1))^((1)(5)) \\ A=661.20 \end{gathered}`

Therefore, total amount after 5 year is $661.20.

Ending Balance = $661.20