Final answer:
The balance in the account after 4 years with a $4,200 deposit at 4.2% interest compounded monthly will be approximately $4,944.41.
Step-by-step explanation:
The balance in the account after 4 years if a $4,200 deposit is earning 4.2% interest, compounded monthly can be calculated using the compound interest formula:
A = P(1 + r/n)(nt)
Where:
- A = the future value of the investment/loan, including interest
- P = the principal investment amount (the initial deposit)
- r = the annual interest rate (decimal)
- n = the number of times that interest is compounded per year
- t = the time the money is invested for, in years
For this particular question:
- P = $4,200
- r = 4.2/100 = 0.042
- n = 12 (since interest is compounded monthly)
- t = 4 years
Hence, the equation becomes:
A = 4200(1 + 0.042/12)(12*4)
Plugging in the numbers:
A = 4200(1 + 0.0035)48
A = 4200(1.0035)48
A ≈ 4200 * 1.17724
A ≈ 4944.41
Therefore, the balance in the account after 4 years would be approximately $4,944.41, rounded to the nearest cent.