Rolfe set up an RRSP for a client when the client was 30 years old. The client put $750 into the account every month until they retired at age 60. The account averaged an annual rate of return of 7.6% per year compounded annually. If the client then wanted to take a monthly disbursement from the account starting at age 60 for the next 25 years, what would the monthly disbursement be if the RRSP investment retained the same terms and after 25 years would have a zero balance?  Value of the account at age 60

This problem involves two main stages:

1. **Accumulation Phase (30 to 60 years old)**: The client deposits \$750 per month for 30 years. The money earns 7.6% interest compounded annually.
2. **Decumulation Phase (60 to 85 years old)**: The client withdraws monthly for 25 years such that the balance reaches zero at age 85.

We'll break this into two parts:

### Part 1: Calculate the value of the RRSP account at age 60
The client contributes monthly for 30 years, so the number of contributions is:

\[
n = 30 \text{ years} \times 12 \text{ months/year} = 360 \text{ payments}
\]

The monthly contribution is \$750, but the interest is compounded annually, so we will use an annual interest rate for calculations.

The future value $FV$ of a series of monthly payments can be calculated using the Future Value of an Annuity formula:

\[
FV = P \times \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right)
\]

Where:
- $P = 750$ (monthly contribution),
- $r = 0.076$ (annual interest rate),
- $t = 30$ years,
- $n = 1$ (since it's compounded annually, not monthly).

First, we'll calculate the future value of the account at age 60.

### Part 2: Calculate the monthly disbursement
Once we know the value of the account at age 60, we need to find the monthly disbursement for the next 25 years. We'll use the Present Value of an Annuity formula to ensure the account is depleted after 25 years, assuming the same interest rate of 7.6% compounded annually.

The formula for the monthly disbursement is:

\[
P = \frac{PV \times r/n}{1 - (1 + r/n)^{-nt}}
\]

Where:
- $PV$ is the value of the account at age 60,
- $r = 0.076$,
- $n = 1$ (since interest is compounded annually),
- $t = 25$ years (withdrawal period).

Let me calculate these values step by step.The value of the RRSP account at age 60 is approximately \$78,973.06.

Next, let's calculate the monthly disbursement the client can receive for the next 25 years, assuming the same interest rate of 7.6%, compounded annually.The monthly disbursement the client can receive for the next 25 years is approximately \$7,146.98, assuming the account retains the same 7.6% annual interest rate and is depleted by the end of the 25-year period.

Would you like further details or clarification on any part of the process?

Here are some related questions:
1. How does compounding frequency affect the future value of investments?
2. What are the benefits of starting an RRSP early?
3. How would the monthly disbursement change with a lower interest rate during the decumulation phase?
4. Can we account for inflation when calculating future disbursements?
5. What happens if the client wants to withdraw for a longer or shorter period?

**Tip**: Regularly reviewing the terms of your RRSP investments can help ensure they meet your long-term goals, especially when retirement approaches.

Rolfe set up an RRSP for a client when the client was 30 years old. The client put $750 into the account every month until they retired at age 60. The account averaged an annual rate of return of 7.6% per year compounded annually. If the client then wanted to take a monthly disbursement from the account starting at age 60 for the next 25 years, what would the monthly disbursement be if the RRSP investment retained the same terms and after 25 years would have a zero balance?

Explore how to calculate the future value of an RRSP account with $750 monthly contributions over 30 years, earning 7.6% annual interest, and determine the monthly disbursement over 25 years. Learn about key financial concepts such as compound interest and annuities.

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