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You deposit $400 each month in a savings plan. The first monthly deposit occurs in month 2 and the final deposit occurs in month 11. What is the accumulated value of your savings in 12 months' time? The interest rate is 18% p.a. compounded monthly. Group of answer choices $4,816.48 $4,281.09 $4,345.30 $3,823.74 $5,216.48

Question

You deposit $400 each month in a savings plan. The first monthly deposit occurs in month 2 and the final deposit occurs in month 11. What is the accumulated value of your savings in 12 months' time? The interest rate is 18% p.a. compounded monthly.

Group of answer choices

$4,816.48

$4,281.09

$4,345.30

$3,823.74

$5,216.48

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Solution

To calculate the accumulated value of your savings in 12 months' time, we can use the formula for the future value of a series of regular payments:

FV = P * [(1 + r)^n - 1] / r

where:

  • FV is the future value
  • P is the regular payment per period ($400)
  • r is the interest rate per period (18% or 0.18 divided by 12)
  • n is the number of periods (10 months, because the first deposit occurs in month 2)

Substituting the given values into the formula, we get:

FV = $400 * [(1 + 0.18/12)^10 - 1] / (0.18/12)

Calculating this expression, we find that the accumulated value of your savings in 12 months' time is approximately 4,816.48.Therefore,thecorrectansweris4,816.48. Therefore, the correct answer is 4,816.48.

This problem has been solved

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