Find the balance in the account after the given period.
$3500 deposit earning 6.75% compounded monthly, after 6 months
a. $3,619.80
b. $3,743.70
c. $3,748.22
d. $4,860.36
P = Po(1+r)^n.
Po = $3500, r = (6.75%/12)/100% =
0.005625 = Monthly % rate expressed as a decimal.
n = 1Comp./mo. * 6mo = 6 Compounding periods.
P = ?.
Oh, finances! Time to put on my money hat and do some calculations. Let's see, we have a deposit of $3500 earning 6.75% compounded monthly over 6 months.
To find the balance, we'll need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial deposit)
r = the annual interest rate (6.75%)
n = the number of times interest is compounded per year (monthly, so 12)
t = the number of years (6 months, so 0.5)
Plugging in all the numbers, we get:
A = 3500(1 + 0.0675/12)^(12*0.5)
Now, time for the circus act! Let's calculate.
The balance after 6 months is approximately $3,748.22. So the answer is c. $3,748.22. Ta-da!
To find the balance in the account after 6 months, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = the interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, the initial deposit (P) is $3500, the interest rate (r) is 6.75% or 0.0675, the interest is compounded monthly (n = 12), and the time period (t) is 6 months or 0.5 years.
Using the formula:
A = $3500(1 + 0.0675/12)^(12*0.5)
A = $3500(1.005625)^(6)
A ≈ $3743.70
So, the balance in the account after 6 months would be approximately $3,743.70.
Therefore, the correct answer is b. $3,743.70.
To find the balance in the account after the given period, we can use the compound interest formula:
A = P * (1 + r/n)^(n*t)
Where:
A = the final balance (what we want to find)
P = the initial deposit ($3500)
r = the annual interest rate (6.75% or 0.0675 as a decimal)
n = the number of compounding periods per year (monthly, so n=12)
t = the number of years of the given period (6 months, so t=0.5)
Now, let's plug in the values into the formula and calculate the balance:
A = 3500 * (1 + 0.0675/12)^(12*0.5)
A = 3500 * (1 + 0.005625)^(6)
A ≈ 3500 * (1.005625)^6
A ≈ 3500 * 1.03490218096
A ≈ 3627.65763486
The balance, rounded to two decimal places, is approximately $3627.66.
Now, let's check the answer choices to find the closest one:
a. $3,619.80
b. $3,743.70
c. $3,748.22
d. $4,860.36
The closest answer to $3627.66 is option b. $3,743.70.
Therefore, the balance in the account after 6 months is approximately $3,743.70 (option b).