Question

You are comparing two annuities with equal present values. The applicable discount rate is 7.25 percent. One annuity pays $2,500 on the first day of each year for 15 years. How much does the second annuity pay each year for 15 years if it pays at the end of each year?

A) $2,331.00
B) $2,266.67
C) $2,500.00
D) $2,390.50
E) $2,681.25.

Answer 1

To find the present value of the second annuity that pays at the end of each year, we can use the formula: Present Value = Cash Flow / (1 + r)^n. Substituting the given values, the second annuity pays $2,266.67 each year for 15 years.

Step-by-step explanation:

To calculate the amount that the second annuity pays each year, we can use the concept of present value. The present value of an annuity is the value of its future cash flows discounted back to the present using a given discount rate. In this case, the discount rate is 7.25 percent.

The present value of the first annuity is given as $2,500 on the first day of each year for 15 years. To find the present value of the second annuity, which pays at the end of each year, we can use the formula:

Present Value = Cash Flow / (1 + r)n

Where:

• Cash Flow = $2,500
• r = Discount Rate = 7.25%
• n = Number of years = 15

Substituting these values into the formula, we get:

Present Value (second annuity) = $2,500 / (1 + 0.0725)15 = $2,266.67

Therefore, the second annuity pays $2,266.67 each year for 15 years.