Kevin has a client who wants to invest in an account that earns 3% interest, compounded annually. The client opens the account with an initial deposit of $5,000, and deposits an additional $5,000 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 tenth deposit is __________.
Question
Kevin has a client who wants to invest in an account that earns 3% interest, compounded annually. The client opens the account with an initial deposit of 5,000 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 tenth deposit is __________.
Solution 1
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Solution 2
To solve this problem, we
Solution 3
To solve this problem, we can use the formula for the future value of a series of payments or annuities compounded annually:
FV = P * [(1 + r)^n - 1] / r
where: FV is the future value of the account, P is the annual deposit, r is the annual interest rate, and n is the number of years.
In this case, P = $5,000, r = 3% or 0.03, and n = 10 years.
Substituting these values into the formula, we get:
FV = $5,000 * [(1 + 0.03)^10 - 1] / 0.03
Solving this equation gives us the future value of the account after the tenth deposit.
First, calculate the value inside the brackets:
(1 + 0.03)^10 - 1 = 1.34392 - 1 = 0.34392
Then, multiply this by the annual deposit and divide by the interest rate:
FV = 57,320
So, the balance of the account after the tenth deposit is approximately $57,320, rounded to the nearest dollar.
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