Question

Find the balance in the account after the given period.$3500 deposit earning 6.75% compounded monthly, after 6 monthsa. $3,619.80b. $3,743.70c. $3,748.22d. $4,860.36show your work thank you

Answer 1

The answer is $3,619.80.

To answer this question, we need to remember that the formula for compound interest is given by:

`A=P(1+(r)/(n))^(nt)`

Where:

• A will be the final balance after the given period (accrued amount).

,

• P is the Principal (the amount we deposit). In this case, we have $3500.

,

• r is the interest rate. In this case, we have 6.75% = 6.75/100.

,

• n is the number of times per year compounded. In this case, the number of times is monthly, that is, n = 12.

,

• t is the time in years. Since we have here that we need the balance after 6 months, we have that 6 months is 1/2 year = 0.5year.

Then we can substitute the corresponding values into the general equation as follows:

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=3500(1+((6.75)/(100))/(12))^{12((1)/(2))} \\ A=3619.79864399 \end{gathered}`

If we round this result to two decimals, we have $3619.80

Using the given equation, we have:

`f(x)=a(1+(r)/(n))^(xn)`

Where:

• a is the initial amount. In this case, a = $3500.

,

• r is the rate (of interest). In this case, r = 6.75% = 6.75/100.

,

• x is the time (in years). Since we have here 6 months, then 6 months is 1/2 year.

,

• n is the number of times per year compounded. In this case, the number of times is monthly, that is, n = 12.

Then we can apply the equation as follows:

x = 1/2

`\begin{gathered} f(x)=a(1+(r)/(n))^(xn) \\ f((1)/(2))=3500(1+((6.75)/(100))/(12))^{((1)/(2))(12)} \\ f((1)/(2))=3619.79864399 \end{gathered}`

If we round our result to the nearest hundredths, we have:

`f((1)/(2))=\$3,619.80`

We need to remember that:

`6.75\%=(6.75)/(100)=0.0675`

And we have that n is the number of times per year compounded. In this case, the number of times is monthly, that is, n = 12. If we have a daily compounded amount, the value for n = 365. If it is quarterly compounded, we have that n = 4, and so on.

We got the same answer in both cases.

In summary, the balance in the account after the given period (6 months) is $3,619.80 (option a) - the interest period was 6 months (1/2 year).