Questions: A deposit of 1200 is added to an account that earns 5% interest, compounded annually. Each year, an additional deposit of 1200 is added to the account. What is the value of the account after the tenth total deposit if no withdrawals or additional deposits are made?

Solution Steps

The future value of the initial deposit is calculated using the formula: $P(1 + r)^n$. Substituting the given values, we get: $1200(1 + 0.05)^10 = 1954.67$

Each annual deposit earns interest for a different number of years. The future value of these deposits can be calculated using the formula for the sum of a geometric series: $D\left(\frac{(1 + r)^n - 1}{r}\right)$. Substituting the given values, we get: $1200\left(\frac{(1 + 0.05)^10 - 1}{0.05}\right) = 15093.47$

The total future value of the account is the sum of the future value of the initial deposit and the future values of all subsequent deposits. Thus, $FV = 1954.67 + 15093.47 = 17048.14$

Final Answer