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

Question

BlackTom AI · Accepted Answer

Question restatement: You receive 223 dollars every month for 12 months, with a discount rate of 0.11. What is the present value (PV) of these payments?

Step 1: Identify the cash flow pattern. This is a level annuity-immediate scenario with 12 monthly payments of 223.

Step 2: Convert the annual discount rate to a monthly period rate. If the given discount rate is annual (0.11), the corresponding monthly rate is i = 0.11 / 12 ≈ 0.0091666667.

Step 3: Use the present value of an ordinary annuity formula for monthly payments: PV = Pmt × [(1 − (1 + i)^−n) / i], where Pmt = 223, i ≈ 0.0091666667, and n = 12.

Step 4: Compute the discount factor component. First calculate (1 + i)^−n = (1.0091666667)^−12. This requires either a calculator or iterative computation; approximately, (1.0091666667)^12 ≈ 1.1156, so its inverse is about 0.896. Therefore, 1 − (1 + i)^−n ≈ 1 − 0.896 = 0.104.

Step 5: Divide by the monthly rate i. Compute 0.104 / 0.0091666667 ≈ 11.34 (approximately, depending on rounding during the intermediate steps).

Step 6: Multiply by the monthly payment to obtain PV. PV ≈ 223 × 11.34 ≈ 2530.42 (approximately, exact value depends on the precision of the intermediate calculations).

Notes on precision and alternative interpretations:
- If a different interpretation of the discount rate is intended (for example, a different compounding convention or treating 0.11 as a monthly rate), the PV result would change accordingly.
- The calculation shown uses a standard monthly rate conversion from an annual rate and applies the ordinary annuity formula. Small differences in rounding during the exponentiation step can shift the final PV by a few dollars.

Summary of the approach: Convert annual rate to a per-period rate, apply the present value of an ordinary annuity formula, compute the annuity factor, and multiply by the monthly payment to obtain the present value.

FINA2720.MERGED.202610 Practice with Respondus and Time Value of Money- Requires Respondus LockDown Browser

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

查看解析

登录即可查看完整答案

类似问题

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 $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?

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

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单