I have been trying to figure out if it is worth cashing in some high interest I-Bonds maturing in 2030 that will make my taxable income huge that year. I decided to ask AI to help. Grok got an error. CoPilot in the Edge browser seemed to handle the question but I think it made a mistake.
I think it did not handle the compounding of interest in scenario 2 correctly because it should have subtracted the tax each year rather than at the end. Maybe I phrased the prompt poorly. I think the final amount for scenario 2 should be lower. Does this make sense?
Here is the prompt:
I have a tax deferred bond worth $23,000 including $18,000 of taxable interest and paying 4% interest per year compounded annually. The basis in this bond is $5000. This bond matures in 5 years and I will have to pay tax at the rate of 24%. If i cash this bond now and pay tax at the rate of 12% on the $18,000 of taxable income and invest the proceeds at a rate of 2% interest and pay tax on this interest each year at the rate of 22% per year. which scenario yields greater value after five years?
Here is the response:
Let’s break down both scenarios to determine which one yields greater value after five years.
Tax Calculation: [ \text{Taxable Interest} = 27,982.95 - 5,000 = 22,982.95 ] [ \text{Tax} = 22,982.95 \times 0.24 = 5,515.91 ]
Net Value: [ \text{Net Value} = 27,982.95 - 5,515.91 = 22,467.04 ]
Proceeds After Tax: [ \text{Proceeds} = 23,000 - 2,160 = 20,840 ]
Future Value Calculation: [ FV = PV \times (1 + r)^n ] [ FV = 20,840 \times (1 + 0.02)^5 ] [ FV = 20,840 \times 1.10408 ] [ FV = 22,999.47 ]
Tax on Interest Earned: [ \text{Interest Earned} = 22,999.47 - 20,840 = 2,159.47 ] [ \text{Tax} = 2,159.47 \times 0.22 = 475.08 ]
Net Value: [ \text{Net Value} = 22,999.47 - 475.08 = 22,524.39 ]
I think it did not handle the compounding of interest in scenario 2 correctly because it should have subtracted the tax each year rather than at the end. Maybe I phrased the prompt poorly. I think the final amount for scenario 2 should be lower. Does this make sense?
Here is the prompt:
I have a tax deferred bond worth $23,000 including $18,000 of taxable interest and paying 4% interest per year compounded annually. The basis in this bond is $5000. This bond matures in 5 years and I will have to pay tax at the rate of 24%. If i cash this bond now and pay tax at the rate of 12% on the $18,000 of taxable income and invest the proceeds at a rate of 2% interest and pay tax on this interest each year at the rate of 22% per year. which scenario yields greater value after five years?
Here is the response:
Let’s break down both scenarios to determine which one yields greater value after five years.
Scenario 1: Hold the Bond Until Maturity
- Current Value of Bond: $23,000
- Interest Rate: 4% compounded annually
- Tax Rate on Maturity: 24%
Tax Calculation: [ \text{Taxable Interest} = 27,982.95 - 5,000 = 22,982.95 ] [ \text{Tax} = 22,982.95 \times 0.24 = 5,515.91 ]
Net Value: [ \text{Net Value} = 27,982.95 - 5,515.91 = 22,467.04 ]
Scenario 2: Cash the Bond Now and Reinvest
- Current Value of Bond: $23,000
- Taxable Interest: $18,000
- Tax Rate on Cashing: 12%
- Reinvestment Rate: 2% compounded annually
- Tax Rate on Interest: 22%
Proceeds After Tax: [ \text{Proceeds} = 23,000 - 2,160 = 20,840 ]
Future Value Calculation: [ FV = PV \times (1 + r)^n ] [ FV = 20,840 \times (1 + 0.02)^5 ] [ FV = 20,840 \times 1.10408 ] [ FV = 22,999.47 ]
Tax on Interest Earned: [ \text{Interest Earned} = 22,999.47 - 20,840 = 2,159.47 ] [ \text{Tax} = 2,159.47 \times 0.22 = 475.08 ]
Net Value: [ \text{Net Value} = 22,999.47 - 475.08 = 22,524.39 ]
Comparison
- Scenario 1 (Hold the Bond): $22,467.04
- Scenario 2 (Cash and Reinvest): $22,524.39