Final answer:
To calculate the future value of a retirement account with monthly deposits of $450 at 10% interest compounded monthly for 30 years, use the future value of an annuity formula with appropriate values for the deposit, interest rate, compounding frequency, and time period.
Step-by-step explanation:
You are planning to make monthly deposits of $450 into a retirement account that pays 10 percent interest compounded monthly. To determine how large your retirement account will be in 30 years, you can use the future value of an annuity formula:
Future Value of Annuity = P × {[ ((1 + r)^nt - 1) / r ]}
Where:
- P is the monthly deposit ($450)
- r is the monthly interest rate (10% annual rate divided by 12 months, so 0.1/12)
- n is the number of times the interest is compounded per year (12)
- t is the number of years (30)
Plugging in the values:
Future Value of Annuity = $450 × {[ ((1 + 0.1/12)^(12×30) - 1) / (0.1/12) ]}
Calculating further:
Future Value of Annuity = $450 × {[ ((1 + 0.008333)^360 - 1) / 0.008333 ]}
The resulting figure will give you the total amount in your retirement account after 30 years. You can do the calculation using a financial calculator or spreadsheet software that has financial functions.