Time Value of Money Solution Grid: Additional Problems

Written by True Tamplin, BSc, CEPF®

Reviewed by Subject Matter Experts

Updated on February 06, 2024

Present Value Calculation Using the Solution Grid

To determine the present value using the solution grid, adhere to these steps:

  1. Recognize the cash flows and their respective time periods.
  2. Establish the suitable discount rate or interest rate.
  3. Locate the point of intersection for each cash flow and its time period on the solution grid.
  4. Aggregate the present values obtained from each intersection to derive the total present value.

Problem 1: You are considering an investment with cash flows of $500 at the end of Year 1, $800 at the end of Year 2, and $1,200 at the end of Year 3. The discount rate is 8%. Calculate the present value of these cash flows using the solution grid.

Solution 1: Using the solution grid, you can calculate the present value as follows:

Present value of $500 at the end of Year 1 = $500 / (1 + 0.08)^1 = $462.96

Present value of $800 at the end of Year 2 = $800 / (1 + 0.08)^2 = $675.68

Present value of $1,200 at the end of Year 3 = $1,200 / (1 + 0.08)^3 = $964.13

Total present value = $462.96 + $675.68 + $964.13 = $2,102.77

Therefore, the present value of the cash flows is approximately $2,102.77.

Problem 2: You have a potential investment that offers cash flows of $1,500 at the end of Year 1, $3,000 at the end of Year 2, and $4,500 at the end of Year 3. The discount rate is 6%. Determine the present value of these cash flows using the solution grid.

Solution 2: To calculate the present value using the solution grid, follow these steps:

Present value of $1,500 at the end of Year 1 = $1,500 / (1 + 0.06)^1 = $1,415.09

Present value of $3,000 at the end of Year 2 = $3,000 / (1 + 0.06)^2 = $2,673.80

Present value of $4,500 at the end of Year 3 = $4,500 / (1 + 0.06)^3 = $3,797.83

Total present value = $1,415.09 + $2,673.80 + $3,797.83 = $7,886.72

Therefore, the present value of the cash flows is approximately $7,886.72

Future Value Calculation Using the Solution Grid

To compute the future value utilizing the solution grid, adhere to these steps:

  1. Recognize the cash flows and their respective time periods.
  2. Establish the suitable interest rate or rate of return.
  3. Locate the point of intersection for each cash flow and its time period on the solution grid.
  4. Aggregate the future values obtained from each intersection to derive the total future value.


Problem 1:
You invest $2,500 at the start of Year 1 with an annual interest rate of 6%. You intend to keep the investment for 3 years. Calculate the future value of your investment using the solution grid.

Solution 1: To determine the future value using the solution grid, follow these steps:

Future value of $2,500 at the end of Year 1 = $2,500 x (1 + 0.06)^1 = $2,650 Future value of $2,500 at the end of Year 2 = $2,500 x (1 + 0.06)^2 = $2,809 Future value of $2,500 at the end of Year 3 = $2,500 x (1 + 0.06)^3 = $2,979.54 Total future value = $2,650 + $2,809 + $2,979.54 = $8,438.54

Therefore, the future value of the investment after 3 years is approximately $8,438.54.

Problem 2: You deposit $3,000 at the beginning of Year 1 into a savings account earning an annual interest rate of 5%. Your plan is to keep the money in the account for 7 years. Calculate the future value of your savings using the solution grid.

Solution 2: To calculate the future value using the solution grid, proceed with these steps:

Future value of $3,000 at the end of Year 1 = $3,000 x (1 + 0.05)^1 = $3,150 Future value of $3,000 at the end of Year 2 = $3,000 x (1 + 0.05)^2 = $3,307.50 Future value of $3,000 at the end of Year 3 = $3,000 x (1 + 0.05)^3 = $3,472.88 Future value of $3,000 at the end of Year 4 = $3,000 x (1 + 0.05)^4 = $3,646.52 Future value of $3,000 at the end of Year 5 = $3,000 x (1 + 0.05)^5 = $3,828.85 Future value of $3,000 at the end of Year 6 = $3,000 x (1 + 0.05)^6 = $4,020.29 Future value of $3,000 at the end of Year 7 = $3,000 x (1 + 0.05)^7 = $4,221.31 Total future value = $3,150 + $3,307.50 + $3,472.88 + $3,646.52 + $3,828.85 + $4,020.29 + $4,221.31 = $25,647.35

Therefore, the future value of your savings after 7 years is approximately $25,647.35.


About the Author

True Tamplin, BSc, CEPF®

True Tamplin is a published author, public speaker, CEO of UpDigital, and founder of Finance Strategists.

True is a Certified Educator in Personal Finance (CEPF®), author of The Handy Financial Ratios Guide, a member of the Society for Advancing Business Editing and Writing, contributes to his financial education site, Finance Strategists, and has spoken to various financial communities such as the CFA Institute, as well as university students like his Alma mater, Biola University, where he received a bachelor of science in business and data analytics.

To learn more about True, visit his personal website, view his author profile on Amazon, or check out his speaker profile on the CFA Institute website.

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