N

Definition

N, in the context of equal payments with a financial calculator and Excel, represents the number of periods or payments over which a loan or investment is made. It is a critical variable in the calculation of annuities and other financial instruments that involve a series of equal periodic payments.

5 Must Know Facts For Your Next Test

1. The value of N is directly proportional to the total amount of interest paid on a loan or investment over the life of the instrument.
2. Increasing the value of N while keeping other variables constant will result in a higher total interest paid, but a lower periodic payment amount.
3. N is a key input in the calculation of the payment amount for an annuity, using the formula: Payment = PV * [c(1+c)^N]/[(1+c)^N-1], where c is the periodic interest rate.
4. In Excel, the PMT function can be used to calculate the periodic payment amount, given the values of PV, N, and the periodic interest rate.
5. Understanding the relationship between N, PV, and the periodic payment amount is crucial for making informed decisions about loans, investments, and other financial instruments.

Review Questions

• Explain how the value of N affects the total interest paid on a loan or investment.
  • The value of N, which represents the number of payment periods, is directly proportional to the total amount of interest paid on a loan or investment. As the value of N increases, the total interest paid over the life of the instrument will also increase, even if the other variables (such as the periodic interest rate and the present value) remain constant. This is because a longer repayment or investment period allows for more compounding of the interest, resulting in a higher total interest cost or return.
• Describe the relationship between N, the periodic payment amount, and the total interest paid on an annuity.
  • In the context of an annuity, where a series of equal periodic payments are made, the value of N is a key determinant of the periodic payment amount and the total interest paid. As the value of N increases, the periodic payment amount decreases, but the total interest paid over the life of the annuity increases. This is because a longer repayment period allows for more compounding of the interest, resulting in a higher total interest cost. Conversely, a shorter repayment period (lower N) will result in higher periodic payments but lower total interest paid.
• Analyze the impact of changing the value of N on the present value and future value of a financial instrument.
  • The value of N has a significant impact on the present value (PV) and future value (FV) of a financial instrument. As the value of N increases, the present value of a series of future payments will decrease, all else being equal. This is because a longer repayment or investment period allows for more compounding of the interest, resulting in a lower present value. Conversely, as the value of N increases, the future value of an investment will increase, as the compounding effect over a longer period of time will result in a higher final value. Understanding the relationship between N, PV, and FV is crucial for making informed decisions about the timing and structure of financial instruments.

Related terms

Annuity: A series of equal payments made at regular intervals, such as monthly or yearly, for a specified number of periods.

Present Value (PV): The current value of a future stream of payments, discounted at an appropriate interest rate.

Future Value (FV): The value of an investment or loan at some point in the future, based on the initial investment and the interest rate.