Final answer:
To calculate the ending balance of an account with $3,330 at 5% interest compounded monthly after 7 years, use the compound interest formula: A = P(1 + r/n)^(nt), with P = $3,330, r = 0.05, n = 12, t = 7. Compute A to find the final amount, rounded to the nearest penny.
Step-by-step explanation:
The student is interested in calculating the ending balance of an account with a starting balance of $3,330 that earns 5% interest compounded monthly after 7 years. To solve this, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:
- P = principal amount (initial investment)
- r = annual interest rate (decimal)
- n = number of times interest is compounded per year
- t = time in years
- A = amount of money accumulated after n years, including interest.
To find the ending balance, substitute the given values into the formula:
P = $3,330, r = 5/100 = 0.05 (since interest rate is given in percentage, we convert it to decimal), n = 12 (since interest is compounded monthly), and t = 7 (for 7 years).
Now, calculate A using the formula:
A = 3330(1 + 0.05/12)^(12*7)
Simplify the expression inside the parentheses and exponents to get the ending balance. Remember, always round to the nearest penny when dealing with currency.