How much will you have in an account after 25 years if you put $1200 per month in the account that earns 7% compounded monthly?
Answer: $
How much will you have after 25 years if you put $1200 per month in the account that instead earns 8% compounded monthly?
Answer: $
Answer (1)
Calculate the monthly interest rate for both 7% and 8% annual rates.
Determine the total number of deposit periods over 25 years.
Apply the future value of an ordinary annuity formula to find the future value for both interest rates.
The future values are approximately $972 , 086.03 at 7% and $1 , 141 , 231.67 at 8%.
Explanation
Problem Setup and Objective We are asked to calculate the future value of an investment account after 25 years, given monthly deposits of $1200 and two different annual interest rates (7% and 8%) compounded monthly. We will use the future value of an ordinary annuity formula to solve this problem.
Future Value Formula The future value of an ordinary annuity formula is given by: F V = P × r ( 1 + r ) n − 1 where:
F V is the future value of the annuity
P is the periodic payment
r is the periodic interest rate
n is the number of periods
Calculating Future Value at 7% For the first case, the annual interest rate is 7%, so the monthly interest rate is: r 1 = 12 0.07 = 0.00583333... The number of periods is: n = 25 × 12 = 300 The periodic payment is: P = 1200 Plugging these values into the future value formula, we get: F V 1 = 1200 × 0.07/12 ( 1 + 0.07/12 ) 300 − 1 F V 1 = 1200 × 0.00583333 ( 1.00583333 ) 300 − 1 F V 1 ≈ 972 , 086.03 So, the future value with 7% interest is approximately $972,086.03.
Calculating Future Value at 8% For the second case, the annual interest rate is 8%, so the monthly interest rate is: r 2 = 12 0.08 = 0.00666666... The number of periods is: n = 25 × 12 = 300 The periodic payment is: P = 1200 Plugging these values into the future value formula, we get: F V 2 = 1200 × 0.08/12 ( 1 + 0.08/12 ) 300 − 1 F V 2 = 1200 × 0.00666666 ( 1.00666666 ) 300 − 1 F V 2 ≈ 1 , 141 , 231.67 So, the future value with 8% interest is approximately $1,141,231.67.
Final Answer After 25 years, with monthly deposits of $1200, the account will have approximately $972,086.03 if it earns 7% compounded monthly, and approximately $1,141,231.67 if it earns 8% compounded monthly.
Examples
Understanding the future value of investments is crucial for financial planning. For instance, if you're saving for retirement, knowing how much your monthly contributions will grow over time helps you set realistic goals. By using the future value of an annuity formula, you can estimate the potential growth of your investments and adjust your savings strategy accordingly. This calculation is also useful for planning education funds or any long-term savings goals, ensuring you reach your desired financial milestones.
