Question

sine has an rrsp that already contains $100,000. she intends to make deposits of $600 at the end of each month for the next 25 years into this rrsp (which pays interest at 8% compounded monthly). when she retires in 25 years (at the age of 65), she intends to withdraw monthly (end of month) payments for the next 30 years (until she is 95). what is the amount of the monthly withdrawal if the rrsp earns 6% compounded semi-annually after she retires? question 7 options: 7760.27 6452.22 8788.92 12323.34

Answer 1

To find the amount of the monthly withdrawal, we can use the formulas for the future value of an annuity. Plugging in the given values, the monthly withdrawal amount is approximately $6,452.22.

Step-by-step explanation:

To find the amount of the monthly withdrawal, we can use the formula for the future value of an annuity:

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

Where:

• FV is the future value
• P is the monthly deposit
• r is the interest rate per period
• n is the number of periods

For the deposits, P = $600, r = 8%/12 = 0.08/12 = 0.00667, and n = 25*12 = 300. Plugging these values into the formula, we get:

FV = $600 * ((1 + 0.00667)^300 - 1) / 0.00667

FV ≈ $198,521.68

Now, we need to find the amount of the monthly withdrawal using the future value of an annuity formula:

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

For the withdrawals, FV = $198,521.68, r = 6%/2 = 0.06/2 = 0.03, and n = 30*12 = 360. Plugging these values into the formula, we get:

P = $198,521.68 * 0.03 / ((1 + 0.03)^360 - 1)

P ≈ $6,452.22

Therefore, the amount of the monthly withdrawal is approximately $6,452.22.