Final answer:
To find the balance A in the account after the given time period t, we can use the formula for compound interest. In this case, the balance after 18 months is approximately $6635.06.
Step-by-step explanation:
To find the balance A in the account after the given time period t, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the balance after time t
- P is the principal amount (initial deposit)
- r is the annual interest rate (in decimal form)
- n is the number of times the interest is compounded per year
- t is the number of years
In this case, we have a $6200 deposit that earns 8.4% annual interest compounded monthly for 18 months. Let's calculate the balance:
P = $6200
r = 8.4% = 0.084
n = 12 (monthly compounding)
t = 18 months = 18/12 = 1.5 years
Substituting these values into the formula:
A = $6200(1 + 0.084/12)^(12*1.5)
Simplifying this calculation, the balance after 18 months is approximately $6635.06.