Final answer:
The balance of a $1,000 deposit with an annual interest rate of 3.75% compounded monthly after 6 years would be approximately $1,246.86 when calculated using the compound interest formula.
Step-by-step explanation:
The balance of a bank account after a certain period can be calculated using the formula for compound interest, which is A = P (1 + r/n)ⁿˣ, where:
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (decimal)
- n is the number of times interest is compounded per year
- x is the time the money is invested for in years
In this case, for a $1,000 deposit at an annual interest rate of 3.75% compounded monthly, we would have:
- P = $1,000
- r = 3.75% or 0.0375
- n = 12 (since the interest is compounded monthly)
- t = 6 years
Now we plug these values into the formula:
A = $1,000 (1 + 0.0375/12)¹²ˣ⁶
Calculating this out:
A = $1,000 (1 + 0.003125)⁷²
A = $1,000 (1.003125)⁷²
A = $1,000 × 1.246856
A ≈ $1,246.86 (after rounding to two decimal places)
So, after 6 years, the balance in the account would be about $1,246.86.