Answer:
To calculate the future value of an annuity with monthly compounding, you can use the formula for the future value of an annuity:
FV = PMT × [(1 + r)^(nt) - 1] / r
Where:
FV is the future value of the annuity.
PMT is the monthly payment.
r is the monthly interest rate (annual interest rate divided by 12, and expressed as a decimal).
n is the number of times the interest is compounded per year (in this case, 12 for monthly compounding).
t is the number of years.
In this case:
PMT = $1,530
r = 0.00475 (monthly interest rate)
n = 12 (monthly compounding)
t = 12 years
Now, plug these values into the formula:
FV = 1530 × [(1 + 0.00475)^(12 × 12) - 1] / 0.00475
Now, calculate the future value:
FV ≈ 1530 × [(1.00475)^144 - 1] / 0.00475 ≈ 1530 × (1.793847 - 1) / 0.00475 ≈ 1530 × (0.793847) / 0.00475 ≈ $256,095.78947
So, after 12 years, there will be approximately $256,095.79 in the account.
To find out how much of this is interest, subtract the total amount deposited (12 years × 12 months × $1,530) from the final amount:
Interest = Total Amount - Total Deposits
Interest = $256,095.79 - (12 × 12 × $1,530)
Interest = $256,095.79 - $219,960
Interest ≈ $36,135.79
So, approximately $36,135.79 of the total amount is interest.