Find the balance in the account after the given period.

Question

$3500 deposit earning 6.75% compounded monthly, after 6 months
(1 point)
Responses

$3,619.80
$3,619.80

$3,743.70
$3,743.70

$3,748.22
$3,748.22

$4,860.36

Answer 1

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 (balance)
P = principal amount (initial deposit)
r = annual interest rate (6.75% = 0.0675)
n = number of times interest is compounded per year (monthly compounding means n = 12)
t = time in years (6 months = 0.5 years)

Plugging in the values:

A = $3500(1 + 0.0675/12)^(12*0.5)
A = $3500(1 + 0.05625)^(6)
A = $3500(1.05625)^(6)
A ≈ $3743.70

Therefore, the balance in the account after 6 months is approximately $3,743.70.

The correct answer is:
$3,743.70