Taylor wants to know how much she needs to have in her RRSP so that she can buy an ordinary annuity that will pay $5,000 every month. For each combination of term and monthly compounded interest rate in the table, calculate the initial amount required to purchase the annuity.
Term of the Annuity	Interest Rate	Initial Amount Needed
10 years	6%	
$0.00
10 years	8%	
$0.00
For full marks your answer(s) should be rounded to the nearest cent.

To determine the initial amount Taylor needs in her RRSP to purchase an ordinary annuity, we can use the Present Value of an Annuity formula:

\[
PV = PMT \times \frac{1 - (1 + i)^{-n}}{i}
\]

where:
- $ PV $ is the present value (initial amount needed),
- $ PMT $ is the annuity payment amount per period,
- $ i $ is the monthly interest rate,
- $ n $ is the total number of payments.

Given:
- Monthly payment $ PMT = 5000 $.
- For 10 years, $ n = 10 \times 12 = 120 $ payments.

Let’s calculate the required initial amount for each interest rate.

### 1. For a 6% annual interest rate compounded monthly:
- Monthly interest rate $ i = \frac{6\%}{12} = 0.5\% = 0.005 $.

\[
PV = 5000 \times \frac{1 - (1 + 0.005)^{-120}}{0.005}
\]

### 2. For an 8% annual interest rate compounded monthly:
- Monthly interest rate $ i = \frac{8\%}{12} = 0.6667\% = 0.006667 $.

\[
PV = 5000 \times \frac{1 - (1 + 0.006667)^{-120}}{0.006667}
\]

Let’s compute these values.The initial amounts Taylor needs to have in her RRSP are as follows:

1. For a 10-year annuity at a 6% interest rate, she needs **$450,367.27**.
2. For a 10-year annuity at an 8% interest rate, she needs **$412,107.40**.

Would you like more details on these calculations or have any questions?

### Related Questions:
1. How would the required initial amount change for a 20-year term?
2. What if the payment amount was $6,000 instead of $5,000?
3. How is the formula affected if interest is compounded quarterly instead of monthly?
4. How would inflation affect the value of these payments over time?
5. What’s the impact of a higher interest rate on the initial amount needed?

### Tip:
The higher the interest rate, the lower the initial amount needed to generate the same annuity payment.

Taylor wants to know how much she needs to have in her RRSP so that she can buy an ordinary annuity that will pay $5,000 every month. For each combination of term and monthly compounded interest rate in the table, calculate the initial amount required to purchase the annuity.
Term of the Annuity Interest Rate Initial Amount Needed
10 years 6% $0.00
10 years 8% $0.00
For full marks your answer(s) should be rounded to the nearest cent.

Learn how to calculate the initial amount needed to purchase an ordinary annuity that pays $5,000 monthly. This example shows the calculations for 10-year annuities at 6% and 8% annual interest rates compounded monthly. Learn the present value of annuity formula and its application.

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