Final answer:
To find the total amount in an account after 5 years with annual deposits and compound interest, you can use the future value of an annuity formula. However, the calculated amount was $28,685.60, which does not match any of the options given. There might be a misunderstanding with the question or provided options.
Step-by-step explanation:
To determine the total amount in the account after 5 years when $4,600 is deposited at the end of each year into an account paying 11 percent interest, we need to calculate the future value of an annuity. An annuity is a series of equal payments made at regular intervals. Since the interest in this question is compounded annually, we will use the formula for the future value of an annuity:
Future Value of Annuity = Pmt × 【((1 + r)^n - 1) / r】
- Pmt is the annual payment, which is $4,600.
- r is the annual interest rate, which is 11% or 0.11.
- n is the number of payments, which is 5 for 5 years.
By substituting our values into the formula, we can calculate the total amount:
Future Value of Annuity = $4,600 × 【((1 + 0.11)^5 - 1) / 0.11】
Calculate the value inside the brackets first:
(1 + 0.11)^5 - 1 = (1.11)^5 - 1 ≈ 1.68596 - 1 = 0.68596
Now divide by 0.11:
0.68596 / 0.11 ≈ 6.236
Multiply by the annual payment:
$4,600 × 6.236 ≈ $28,685.60
However, since this result is not one of the options provided, it is possible that the question implies a different calculation method or there might be an error in the options given. In real-world scenarios, calculations can be affected by the timing of the deposits, the exact formula used, and other variables not mentioned in the question.