Paula has a client who wants to invest into an account that earns 4% interest, compounded annually. The client opens the account with an initial deposit of $4,000, and deposits an additional $4,000 into the account each year thereafter.Assuming no withdrawals or other deposits are made and that the interest rate is fixed, the balance of the account (rounded to the nearest dollar) after the eighth deposit is __________.a.)$188,247b.)$102,713c.)$36,857d.)$40,969
Question
Paula has a client who wants to invest into an account that earns 4% interest, compounded annually. The client opens the account with an initial deposit of 4,000 into the account each year thereafter.Assuming no withdrawals or other deposits are made and that the interest rate is fixed, the balance of the account (rounded to the nearest dollar) after the eighth deposit is __________.a.)102,713c.)40,969
Solution
To solve this problem, we need to use the formula for the future value of a series of payments or annuities. The formula is:
FV = P * [(1 + r)^nt - 1] / r
where: FV = future value of the investment P = amount deposited each year r = interest rate n = number of times interest is compounded per year t = number of years
In this case: P = $4,000 r = 4% or 0.04 n = 1 (since interest is compounded annually) t = 8 years
Substituting these values into the formula, we get:
FV = $4,000 * [(1 + 0.04)^8 - 1] / 0.04
Solving this equation gives us the future value of the investment after 8 years.
Let's calculate:
FV = 4,000 * [1.3686 - 1] / 0.04 FV = 36,860
So, the balance of the account after the eighth deposit, rounded to the nearest dollar, is approximately $36,860.
Therefore, the correct answer is c.) $36,857.
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