Final answer:
To find the balance after 3 years and 2 months on a $3,750.00 deposit with a 4% annual interest rate compounded monthly, use the compound interest formula A = P(1 + r/n)^(nt). The calculation results in a final balance of approximately $4,263.72.
Step-by-step explanation:
The student's question concerns finding the balance of a bank account after a certain period of time given an initial deposit and an interest rate. Since the interest is compounded monthly, we need to use the compound interest formula to calculate the future value of the deposit:
The formula for compound interest is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after time t, including interest.
- P is the principal amount (the initial sum of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
In this example, the principal amount (P) is $3,750.00, the annual interest rate (r) is 4% or 0.04 in decimal, the number of times interest is compounded per year (n) is 12 (monthly), and the time (t) is 3 years and 2 months, which is equivalent to 3 + 2/12 or 3.1667 years.
Plugging those numbers into the formula gives us:
A = $3,750.00 * (1 + 0.04/12)^(12*3.1667)
Calculating the expression inside the parentheses first:
1 + 0.04/12 = 1.003333...
Then raising this to the power of (12*3.1667):
(1.003333...)^(12*3.1667) = 1.136992...
Finally, multiplying this by the principal amount gives us the balance after 3 years and 2 months:
A = $3,750.00 * 1.136992...
A ≈ $4,263.72
Therefore, the balance in the account after 3 years and 2 months would be approximately $4,263.72.