Question

Mr. williams expects to retire in 30 years and would like to accumulate $1 million in his pension fund. if the annual interest rate is 12% apr, how much should mr. williams put into his pension fund each month in order to achieve his goal? (assume that mr. williams will deposit the same amount each month into his pension fund, using monthly compounding.)

Answer 1

To accumulate $1 million in his pension fund, Mr. Williams should put approximately $283.26 into his pension fund each month.

Step-by-step explanation:

To calculate how much Mr. Williams should put into his pension fund each month, we can use the formula for the future value of an ordinary annuity: FV = P × ((1 + r)^(n*t) - 1) / r

Where:

• FV is the future value of the annuity ($1,000,000)
• P is the monthly payment
• r is the monthly interest rate (0.12/12 = 0.01)
• n is the number of times the interest is compounded per period (monthly)
• t is the number of periods (30 years × 12 months/year)

Plugging in the values, we get: $1,000,000 = P × ((1 + 0.01)^(12*30) - 1) / 0.01

Solving for P, we find that Mr. Williams should put approximately $283.26 into his pension fund each month.

Answer 2

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