Question

Suppose you want to have $500,000 for retirement in 30 years, and your account earns 8% interest. How much would you need to deposit in the account each month?

a) $1,168.53
b) $1,241.86
c) $1,325.12
d) $1,412.75

Answer 1

To have $500,000 for retirement in 30 years with an 8% interest rate, you would need to deposit approximately $1,325.12 into the account each month.

Step-by-step explanation:

To calculate the amount needed to deposit each month, you can use the future value of an ordinary annuity formula:

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

Where:

• FV = future value ($500,000)
• P = deposit amount per month (unknown)
• r = interest rate per period (8% divided by 12 to get monthly rate)
• n = number of periods (30 years multiplied by 12 months)

Plugging in these values, we get:

FV = P * [(1 + (0.08 / 12))^(30 * 12) - 1] / (0.08 / 12)

Solving for P, we find that P is approximately $1,325.12.

Answer 2

To find out how much to deposit each month to have $500,000 in 30 years with an 8% interest rate, use the future value of an annuity formula and rearrange it to solve for the monthly payment. A financial calculator or spreadsheet can help perform the calculation to choose the correct option.

Step-by-step explanation:

To determine how much money you would need to deposit each month to have $500,000 for retirement in 30 years with an account that earns 8% interest, you can use the future value of an annuity formula:

FV = P × { [{(1 + r)^n - 1} / r] × (1 + r) }

Where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the total number of payments. The monthly interest rate is the yearly rate divided by 12, which is 0.08/12 in this case. The total number of payments for 30 years is 30 × 12.

Rearranging this formula to solve for P, we can calculate the necessary monthly deposit. Plugging in the known values into this rearranged formula will provide the correct monthly deposit amount. You can use a financial calculator or spreadsheet software to perform this calculation.

Given the options provided and recognizing that they represent monthly deposit amounts, we determine that one of them is the correct amount that will achieve the retirement goal with the given interest rate and time frame.