Question
What values do I enter for N, PMT, i/y, FV and PV on a finance calculator to solve for the question below.
What is the value today of a money machine that will pay $3,593.00 every six months for 28.00 years? Assume the first payment is made six months from today and the interest rate is 14.00%.
What is the value today of a money machine that will pay $3,593.00 every six months for 28.00 years? Assume the first payment is made six months from today and the interest rate is 14.00%.
Answers
GPT-4o mini
To find the present value (PV) of the money machine that pays $3,593.00 every six months for 28 years with an annual interest rate of 14%, you will use a financial calculator with the following values:
1. **N** (number of periods):
Since payments are made every six months for 28 years, the number of periods will be:
\[ N = 28 \text{ years} \times 2 \text{ (payments per year)} = 56 \text{ periods} \]
2. **PMT** (payment):
The payment is the cash flow received per period, which is:
\[ PMT = 3,593.00 \]
3. **i/y** (interest rate per period):
The annual interest rate is 14%. Since payments are made semi-annually, you will need to divide the annual rate by 2:
\[ i/y = \frac{14.00\%}{2} = 7.00\% = 0.07 \]
4. **FV** (future value):
Since we are calculating the present value of an annuity, the future value is not a consideration here, so you can set it to:
\[ FV = 0 \]
5. **PV** (present value):
This is what you are solving for, and you will calculate it based on the other values.
In summary:
- N = 56
- PMT = 3,593.00
- i/y = 7.00
- FV = 0
- PV = ?
Once these values are entered into the finance calculator, you can compute the present value (PV).
1. **N** (number of periods):
Since payments are made every six months for 28 years, the number of periods will be:
\[ N = 28 \text{ years} \times 2 \text{ (payments per year)} = 56 \text{ periods} \]
2. **PMT** (payment):
The payment is the cash flow received per period, which is:
\[ PMT = 3,593.00 \]
3. **i/y** (interest rate per period):
The annual interest rate is 14%. Since payments are made semi-annually, you will need to divide the annual rate by 2:
\[ i/y = \frac{14.00\%}{2} = 7.00\% = 0.07 \]
4. **FV** (future value):
Since we are calculating the present value of an annuity, the future value is not a consideration here, so you can set it to:
\[ FV = 0 \]
5. **PV** (present value):
This is what you are solving for, and you will calculate it based on the other values.
In summary:
- N = 56
- PMT = 3,593.00
- i/y = 7.00
- FV = 0
- PV = ?
Once these values are entered into the finance calculator, you can compute the present value (PV).