Final answer:
The amount in the annuity account after 4 years is approximately $114,414.93, and the amount of interest earned is approximately $10,110.93. The calculations were based on monthly compounding at an annual rate of 5.4% with monthly deposits of $2,173.
Step-by-step explanation:
To answer how much is in the annuity account after 4 years and how much of this is interest, we'll use the future value formula for an annuity with monthly compounding interest:
The future value of an annuity formula is given by:
FV = P × ¶·¶((1 + r/n)^(nt) - 1) / (r/n)
Where:
- FV = future value of the annuity
- P = monthly payment (in this case, $2,173)
- r = annual interest rate (in this case, 5.4% or 0.054)
- n = number of times the interest is compounded per year (in this case, 12)
- t = the number of years the money is invested (in this case, 4)
Putting these values into the formula, the calculation is:
FV = $2,173 × ¶·¶((1 + 0.054/12)^(12×4) - 1) / (0.054/12)
Using a calculator, we find that the future value FV is approximately $114,414.93.
The total amount of interest earned is the future value minus the total amount deposited:
Interest = FV - (P × n × t)
Interest = $114,414.93 - ($2,173 × 12 × 4)
Interest = $114,414.93 - $104,304
Thus, the amount of interest earned is approximately $10,110.93.