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At the start of each year for the past 10 years, carol, who is cheryl and barbara's aunt, has put $1,000 into an account earning 4% annually for their benefit. how much is the account worth today, and which process must take place to calculate the value?

A) $12,864.35; annuitizing
B) $17,762.93; compounding
C) $12,486.35; annuitizing
D) $12,006.11; compounding

User Arnstein
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1 Answer

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Final answer:

To determine the value of the investment account after Carol's annual contributions for 10 years at a 4% interest rate, we use the future value of an annuity due formula. The calculated value is approximately $11,494.71, which differs from the provided choices, suggesting a possible question or option mismatch. The process involved in arriving at this value is compounding.

Step-by-step explanation:

The question pertains to the calculation of the future value of an annuity, where Carol makes regular deposits into an account. Since Carol deposits $1,000 at the beginning of each year for 10 years into an account that yields 4% interest annually, we can calculate the future value using the formula for the future value of an annuity due because the payments are made at the start of the period:

FV = P × {[(1 + r)^n - 1] / r} × (1 + r)

Where FV is the future value of the annuity, P is the annual payment, r is the interest rate per period, and n is the number of periods.

Using these numbers, the calculation is as follows:

FV = $1,000 × {[(1 + 0.04)^10 - 1] / 0.04} × (1 + 0.04) ≈ $11,494.71

However, none of the given choices match this calculated value, hence, there might be a misunderstanding of the question or the provided choices might be incorrect.

The process that must take place to calculate the value of this investment account is known as compounding, specifically for an annuity due, since calculations involve payments at the start of each period.

User Cammace
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