Question

A principal amount of $5,000 will be placed in a savings account. A simple interest account earns an annual percentage rate of 6.8%, while a compound interest account has an APR of 3.7% compounded quarterly. Which account has a larger balance after 20 years?

The compound interest account has a larger balance of $11,800.
The simple interest account has a larger balance of $10,444.09.
The simple interest account has a larger balance of $11,800.
The compound interest account has a larger balance of $10,444.09.

Answer 1

Ay dios mío

Answer 2

Give me a sec, this is a gigantic interest amount for SO much time.

Answer 3

\begin{enumerate}
\item The compound interest account has a larger balance of $11,800.
\item The simple interest account has a larger balance of $10,444.09.
\item The simple interest account has a larger balance of $11,800.
\item The compound interest account has a larger balance of $10,444.09.
\end{enumerate}

Now to compare the two savings accounts, you can use the formuIas for simple interest and compound interest:

For simple interest, the formuIa I'm using is:

\[
A_{\text{simple}} = P \left(1 + rt\right)
\]

This is for "Where":
\(A_{\text{simple}}\) = the future value of the investment, including interest
\(P\) = the principal investment amount = $5,000
\(r\) = the annual interest rate (decimal) = 6.8% or 0.068
\(t\) = the time the money is invested for, in years = 20 years

Now, you'll calculate the future value for the simple interest account like this 👇

\[
A_{\text{simple}} = 5,000 \left(1 + 0.068 \cdot 20\right) = 5,000 \cdot 2.36 = \$11,800
\]
Now that we got that crap out the way, we'll move to the compound interest 🤏🤓

For compound interest, the formula I'm using is:

\[
A_{\text{compound}} = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where (same thing as before):
\(A_{\text{compound}}\) = the future value of the investment, including interest
\(P\) = the principal investment amount = $5,000
\(r\) = the annual interest rate (decimal) = 3.7% or 0.037
\(n\) = the number of times that interest is compounded per year = 4 (quarterly)
\(t\) = the time the money is invested for, in years = 20 years

Now finally you'll calculate the future value for the compound interest account:

\[
A_{\text{compound}} = 5,000 \left(1 + \frac{0.037}{4}\right)^{4 \cdot 20} \approx 5,000 \cdot 1.2391 \approx \$6,195.47
\]

Then cmparing the two future values 👇

The compound interest account has a larger balance of $6,195.47 compared to the regular interest account's balance of $11,800. Now the summarized answer is down below 👇

The simple interest account has a larger balance of $11,800. 👌 😎

Answer 4

Comparing*

Answer 5

Great, I have more questions-

Answer 6

Just gonna post it here because I'm lazy

Answer 7

A principal amount of $400 is placed in a savings account with an annual rate of 5.75% simple interest for 8 years. Which formula would correctly determine the final amount?

A = (400)(0.0575)(8)
A = (400)(5.75)(8)
A = (400)(5.75)(8) + 400
A = (400)(0.0575)(8) + 400

Answer 8

A principal amount of $900 will be placed in a savings account for 13 years with an APR of 2.9%. What is the difference in the total account balances if simple interest is applied, compared to monthly compounded interest?

$972.22
$339.30
$72.22
$27.22

Answer 9

Essentially the same thing as the previous problems.

Answer 10

I uh got the same question and did that answer the previous time and it said it was wrong-

Answer 11

Yup

Answer 12

Or at least on the previous submission I did it was so-

Answer 13

Got another answer for me here?

Answer 14

I hope most of these are right or I will cry, because I have a borderline D in this class.

Answer 15

I got a 57

Answer 16

No no the assignment was graded as a 57.

Answer 17

Yeah my mums gonna murder me again whew

Answer 18

Yeah and it was my last submission sooo-

Answer 19

Not your fault my cousin had no clue what he was doing for two of em so

Answer 20

A small business owner has decided to invest some of the business profits to save for retirement. A total of $25,000 is invested with a continuously compounded annual interest rate of 2.9%. What is the total account balance after 20 years?

$39,500
$46,450.96
$44,557.63
$44,650.96

Answer 21

A public relations writer received a promotion that came with a $5,000 salary increase. The writer wants to invest the money in a savings account with an annual interest rate of 5.4% for 10 years. How much interest would the account earn with simple interest and with monthly compounded interest?

The account will earn $2,700 in simple interest and $3,569.65 in compound interest.
The account will earn $3,569.65 in simple interest and $2,700 in compound interest.
The account will earn $2,070 in simple interest and $3,580.03 in compound interest.
The account will earn $3,580.03 in simple interest and $2,070 in compound interest.

Answer 22

the four ones that are separated from the top text-

Answer 23

A recent high school graduate is taking out a $2,500 loan to pay for a technical education program. The loan will accrue simple interest until repayment begins in 2 years. If the graduate wants to cap the accrued interest at $150, what interest rate is needed?

30%
5.7%
3%
0.3%

Answer 24

The equation A = (400)(0.053)(5) + (400) represents the amount of money earned on a simple interest savings account. What does the value 400 represent?

Time
Principal amount
Interest rate
Final amount

Answer 25

A wedding photographer has been saving money to use for travel during retirement. The photographer plans to invest in a continuously compounded savings account with an annual interest rate of 4.3%. If the photographer wants to have a total account balance of $40,000 after 20 years, what principal amount must initially be invested?

$23,073.52
$26,020.36
$13,979.64
$16,926.48