To calculate the additional payments needed in 2008 and 2009 for the specified monthly annuity and to determine the suitability of the payments over a 15-year and 20-year term, we need to analyze the annuity structure. However, the information provided may need further clarification in certain areas. Here’s how you might approach the problem:
Step 1: Understanding the Annuity
An annuity is a financial product that can provide a stream of payments over a specific period. The monthly payment of $1,336.72 beginning in December 2012 suggests that the annuity was designed to pay out either for life or a certain number of years.
Step 2: Define Key Variables
- Original Investment: $43,766
- Monthly Payment: $1,336.72
- Interest Rate Association: 5-Year Treasury (this will be used to estimate the annuity's growth).
- Ages: Individual was 96 years old in 2012, 87 years old at the beginning of 2023 and passed away on 3/7/2023.
Step 3: Calculate Total Payments from the Annuity
We can estimate the total payments received from December 2012 to March 2023:
- Monthly payments from December 2012 to March 2023 (about 126 months) = 126 × $1,336.72 = $168,077.92
Step 4: Determine Additional Payments Required
To calculate how much additional money would be necessary in the years 2008 and 2009 to achieve the goal of a monthly payment of $1,336.72, we would model this under the assumption of expected interest rates.
Assuming an average annual return based on the 5-year Treasury yield during your specified period, you would:
- Determine an assumed effective rate of return (for instance, let’s say it’s around 2%).
- Calculate the present value of the future payment stream ($1,336.72/month for an estimated 15 or 20 years) and see what lump sum investment would have been required at that interest rate to fund those payments.
Example Calculation for Present Value (PV) Using Interest
Using the formula for the present value of an annuity: \[ PV = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \] Where:
- \( PMT \) = monthly payment ($1,336.72)
- \( r \) = monthly interest rate (annual rate / 12)
- \( n \) = number of total payments
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For example, over a 20-year term (240 months):
- Assume an interest rate of 2% annually: \( r = \frac{0.02}{12} = 0.0016667\)
- Calculate \( PV \): \[ PV = 1336.72 \times \left( \frac{1 - (1 + 0.0016667)^{-240}}{0.0016667} \right) \approx 1,336.72 \times 146.650 \approx 195,040.82 \]
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Then, to receive this \( PV \) from an investment, we must compare the current investment with the required investment to meet this future value in 2008/2009, adjusted for the time value of money.
Step 5: Developing Additional Payment Adjustments for 2008/2009
Once we have the present value of the future payments identified for both 15- and 20-year terms, you will need to identify how much additional investment was necessary in those years. This can involve creating a formula or financial model considering the cash flows and how additional investments would compound over time to ultimately meet the annuity payment desire.
Please note that the information and calculations provided are illustrative. To perform a precise calculation, you would ideally work with actual historical rates and perhaps consider consulting a financial advisor to get exact figures based on the provided data and your specific financial context.