Answer:
Explanation:
The balance of the savings account after 48 months can be calculated using the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A is the balance after t years
P is the principal (initial amount)
r is the interest rate (as a decimal)
n is the number of times compounded per year
t is the number of years
Step-by-step, the calculation is as follows:
Convert the interest rate from a percentage to a decimal:
r = 7% = 0.07
Determine the number of times compounded per year:
n = 2 (compounded semi-annually)
Determine the number of years:
t = 48 months / 12 months/year = 4 years
Plug the values into the formula:
A = P * (1 + r/n)^(nt)
A = $3500 * (1 + 0.07/2)^(2 * 4)
Calculate the balance using the formula:
A = $3500 * (1.035)^8
A = $3500 * 1.306769
A = $4588.72
So, the balance in the savings account after 48 months is $4588.72.