Question

How much must be deposited at the beginning of each year in an account that pays 10%, compounded annually, so that the account will contain $36,000 at the end of 4 years? (Round your answer to the nearest cent.)

Answer 1

To have an account contain $36,000 at the end of 4 years with 10% interest compounded annually, approximately $8,117.42 must be deposited at the beginning of each year.

Step-by-step explanation:

To find out how much must be deposited at the beginning of each year in an account that pays 10% interest compounded annually, we can use the formula for the future value of an ordinary annuity. The formula is:

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

Where FV is the future value, PMT is the annual deposit, r is the interest rate, and n is the number of years.

In this case, we need to find the value of PMT. The future value (FV) is given as $36,000, the interest rate (r) is 10%, and the number of years (n) is 4. Plugging these values into the formula, we have:

36,000 = PMT * [((1 + 0.10)^4 - 1) / 0.10]

Now, we can solve for PMT:

PMT = 36,000 / [((1.10)^4 - 1) / 0.10]

PMT ≈ $8,117.42