Final answer:
To find the value of the annuity, use the formula Future Value = P((1 + r)^n - 1)/r, where P is the periodic deposit, r is the interest rate per period, and n is the number of periods. Plugging in the given values, the annuity is approximately $134,708. To find the interest, subtract the sum of all the periodic deposits from the future value of the annuity. The interest is approximately $35,708.
Step-by-step explanation:
To find the value of the annuity, we can use the formula:
Future Value = P((1 + r)^n - 1)/r
Where:
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- P is the periodic deposit, which is $3000 in this case
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- r is the interest rate per period, which is 6% compounded annually
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- n is the number of periods, which is 30 years
Plugging in these values into the formula, we can calculate the value of the annuity:
Future Value = $3000((1 + 0.06)^30 - 1)/0.06
Rounding to the nearest dollar, the value of the annuity is approximately $134,708.
To find the interest, we can subtract the sum of all the periodic deposits from the future value of the annuity:
Interest = Future Value - (P * n)
Plugging in the values:
Interest = $134,708 - ($3000 * 30)
Rounding to the nearest dollar, the interest is approximately $35,708.