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It takes 3 years to be vested in your ordinary annuity retirement system. You deposit $500 quarterly into your retirement account that pays 7% interest compounded quarterly. What is the future value of the account in 3 years?

A) $15,827.47
B) $16,512.69
C) $17,274.50
D) $18,104.32

User Corvid
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1 Answer

4 votes

Final answer:

The future value of the annuity is calculated with the formula FV = P × ((1 + r)^n - 1)/r, where P is the periodic payment, r is the quarterly interest rate, and n is the total number of payments. After calculation, the obtained future value does not match the options, indicating a potential error in the options or a requirement for recalibration of inputs.

Step-by-step explanation:

The student's question involves calculating the future value of an ordinary annuity with deposits made quarterly and interest compounded quarterly over a period of 3 years. We are given that the quarterly deposit is $500 and the interest rate is 7% per annum. To solve this, we can use the future value of an annuity formula:

FV = P × rac{((1 + r)^n - 1)}{r}

Where:

  • P is the periodic payment (quarterly deposit)
  • r is the interest rate per period (quarterly)
  • n is the total number of payments (number of quarters)

In our case, P = $500, r = 0.07/4 (since it's compounded quarterly), and n = 3 × 4 = 12 quarters. Thus, the future value is calculated as follows:

FV = 500 × rac{((1 + 0.0175)^12 - 1)}{0.0175} = $7,357.19

Note: The calculated value does not match any given options, which suggests a possible error in the provided options or the need to recheck the calculations and adjustments.

User Akalenuk
by
8.4k points
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