Question

4-49. Consider the accompanying cash-flow diagram. (See Figure P4-49.) (4.7) a. If P-$1,000, A-$200, and 1%-12% per year, then N ? b. If P = $1,000, A = $200, and N = 10 years, then c. If A = $200, i% = 12% per year, and N = 5 years, d. If P $1,000, i% 12% per year, and N 5 years, then P? then A ?

Answer 1

The student's question involves finding the number of periods (N), the annuity payment (A), the interest rate (i%), and the present value (P) in various cash-flow scenarios. These calculations are based on the present value of an annuity formula and involve finance and applied mathematics principles.

Step-by-step explanation:

The student's question pertains to the calculation of unknown variables in cash-flow problems using the concepts of present and future value, annuities, and interest rates. The student is provided with various financial scenarios and is required to solve for missing terms such as the number of periods (N), the annuity payment (A), and the present value (P) when other factors are known. These types of problems typically fall under the domain of finance, a branch of applied mathematics.

When solving for N, the number of periods, we will use the formula for the present value of an annuity. For part b, where we need to calculate i%, the interest rate, we can either use a financial calculator or iterate through the formula until we find the closest interest rate that satisfies the equation. Part c, finding P, the present value for a series of future payments, requires the use of the present value of annuity formula. Lastly, for part d, we calculate A, the annuity payment, using the values given for present value, interest rate, and the number of periods.