Table of contents

1. Introduction to Accounting1h 21m
2. Transaction Analysis1h 13m
3. Accrual Accounting Concepts2h 38m
4. Merchandising Operations2h 30m
5. Inventory1h 55m
6. Internal Controls and Reporting Cash1h 16m
7. Receivables and Investments3h 8m
8. Long Lived Assets5h 1m
9. Current Liabilities2h 19m
10. Time Value of Money1h 23m
- Time Value of Money Equations
  35m
- Using Time Value of Money Tables
  47m
11. Long Term Liabilities2h 45m
12. Stockholders' Equity2h 15m
13. Statement of Cash Flows2h 24m
14. Financial Statement Analysis5h 25m
15. GAAP vs IFRS56m

10. Time Value of Money

Time Value of Money Equations

Financial Accounting

10. Time Value of Money

Time Value of Money Equations

Previous problemNext problem

Struggling with Financial Accounting?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Which of the following equations correctly calculates the future value ($FV$) of $1,000 invested today for 3 years at 5\% annual interest compounded annually?

$FV = 1,000 \times (1 - 0.05)^3$

$FV = 1,000 \times (1 + 0.05)^3$

$FV = 1,000 \div (1 + 0.05)^3$

$FV = 1,000 \times (1 + 0.05 \times 3)$

Previous problemNext problem

Verified step by step guidance

Understand the concept of future value (FV): Future value is the value of a current amount of money at a future date, based on a specific interest rate and compounding frequency. The formula for FV with annual compounding is $FV = PV \times (1 + r)^n$, where $PV$ is the present value, $r$ is the annual interest rate, and $n$ is the number of years.

Analyze the given options: The first option, $FV = 1,000 \times (1 - 0.05)^3$, incorrectly uses subtraction instead of addition in the formula, which is not valid for compounding interest. The second option, $FV = 1,000 \times (1 + 0.05)^3$, correctly follows the formula for future value with annual compounding. The third option, $FV = 1,000 \div (1 + 0.05)^3$, represents a formula for present value, not future value. The fourth option, $FV = 1,000 \times (1 + 0.05 \times 3)$, assumes simple interest rather than compounding, which is incorrect for this scenario.

Identify the correct formula: The correct formula for future value with annual compounding is $FV = PV \times (1 + r)^n$. In this case, $PV = 1,000$, $r = 0.05$, and $n = 3$. This matches the second option: $FV = 1,000 \times (1 + 0.05)^3$.

Explain why compounding is used: Compounding means that interest is calculated not only on the initial principal but also on the accumulated interest from previous periods. This is why the formula includes $(1 + r)^n$, where the exponent $n$ accounts for the number of compounding periods.

Summarize the solution: The correct formula for calculating the future value of $1,000 invested today for 3 years at 5% annual interest compounded annually is $FV = 1,000 \times (1 + 0.05)^3$. This formula accounts for the compounding effect over the specified time period.