If you receive $172 each quarter for 15 years and the discount rate is 0.11, what is the present value?

Question

If you receive $172 each quarter for 15 years and the discount rate is 0.11, what is the present value?

BlackTom AI · Accepted Answer

First, identify what is being asked: the present value of a series of equal payments received periodically. Here, you receive 172 dollars every quarter for 15 years, and the discount rate is 0.11.
To use the standard present-value of an ordinary annuity formula for periodic payments, convert the annual rate to the per-period rate and count the total number of periods.
Step 1: Determine the per-period rate. If 0.11 is an annual rate with quarterly compounding, the quarterly rate is 0.11 / 4 = 0.0275 (2.75% per quarter).
Step 2: Determine the number of periods. There are 15 years with quarterly payments, so n = 15 * 4 = 60 quarters.
Step 3: Apply the present-value of an ordinary annuity formula: PV = Pmt × [1 − (1 + i)^−n] / i, where Pmt = 172, i = 0.0275, n = 60.
Step 4: Compute (1 + i)^−n. Evaluate (1.0275)^60 and then take the reciprocal to get its negative power. Using natural-log approximation: ln(1.0275) ≈ 0.027134, so ln[(1.0275)^60] ≈ 60 × 0.027134 ≈ 1.62804, and (1.0275)^60 ≈ e^1.62804 ≈ 5.10. Therefore (1.0275)^−60 ≈ 1/5.10 ≈ 0.196.
Step 5: Compute the annuity factor: [1 − 0.196] / 0.0275 ≈ 0.804 / 0.0275 ≈ 29.26.
Step 6: Multiply by the payment amount: PV ≈ 172 × 29.26 ≈ 5032.72.
Thus, under these standard assumptions, the present value is approximately 5033 dollars (to the nearest dollar).
Notes and alternative interpretations:
- If 0.11 is an effective quarterly rate (not typical, but possible in some contexts), i_q would be 0.11, n = 60, and PV would be 172 × [1 − (1.11)^−60] / 0.11, which would yield a different value.
- If 0.11 is the nominal annual rate with a different compounding convention than quarterly, the per-period rate would change accordingly, leading to a different PV.
- The value 5273.36 corresponds to a different interpretation of the rate or timing (for example, a different per-period rate or whether payments are at the beginning or end of periods). If the problem specifies a particular compounding convention or timing (e.g., payments at the start of each quarter), you would adjust the formula to an annuity-due variant, which changes the result slightly.
In summary, with standard quarterly compounding of an 11% annual rate and ordinary annuity timing, the present value is about 5033.

FINA3401.13791.202610 Practice with Respondus and Time Value of Money- Requires Respondus LockDown Browser

If you receive $172 each quarter for 15 years and the discount rate is 0.11, what is the present value?

View Explanation

Log in for full answers

Similar Questions

If you receive $99 each quarter for 8 years and the discount rate is 0.1, what is the present value?

If you receive $102 each month for 4 years and the discount rate is 0.06, what is the present value?

If you receive $223 each month for 12 months and the discount rate is 0.11, what is the present value?

If you receive $58 each quarter for 15 years and the discount rate is 0.09, what is the present value?

If you receive $193 each month for 12 months and the discount rate is 0.05, what is the present value?

What is the present value (to the nearest dollar) of a six-period annuity of $300 per year that begins three years from today if the discount rate is 8%?[Fill in the blank]

What is the maximum that should be invested in a project at time zero if the inflows are estimated at $25,000 annually for four years, and the cost of capital is 9%?[Fill in the blank]

If you receive $197 each month for 21 years and the discount rate is 0.03, what is the present value?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler