Chapter 4.2® - Compounding Interest Homework Problem & Time Value of Money Continued - Future Value Formula, Growth of $100 & Future Value Comparisons

• Part 4.1 - Time Value of Money, Future Values of Compounding Interest, Investing for more than 1 Period & Examination of Original Investment & Growth of Investment
• Part 4.2 - Compounding Interest Homework Problem & Time Value of Money Continued - Future Value Formula, Growth of $100 & Future Value Comparisons
• Part 4.3 - How to Use a Financial Calculator BAII Plus to Perform Time Value of Money & Present / Future Value Calculations
• Part 4.4 - Changing Advanced Function Keys (BGN, C/Y, P/Y), Converting from Nominal Interest to Effective Interest Rates using BAII Financial Calculator
• Part 4.5 - Examples of Interest Rate Calculations & Practice Questions #1 - #7
• Part 4.6 - Nominal to Effective Interest Rate Calculations & Practice Questions #8 - #16
• Part 4.7 - Present Value & Discounting – We Know the Future Value, how do we find the Present Value? Single Period Case & PV Discounting for Multiple Periods
• Part 4.8 - An Example of Present Value Discounting & Saving Up Money & Deriving the Basic Present Value Equation
• Part 4.9 - Determining the Discount Rate using Basic Present Value equation & Finding the Number of Accounting Periods
• Part 4.10 - Summary of Time Value Formulas & Calculations
• Part 4.11 - Discounted Cash Flow Valuations - Future Value of Multiple Cash Flows & Designing the Cash Flows Timeline
• Part 4.12 - Compound the Accumulated Balance Forward One Year at a Time - Discounted Cash Flow Valuation - Determining Present Value of Multiple Future Cash Flows & Designing a Financial Timeline
• Part 4.13 - Determining Present Value of Multiple Future Cash Flows – Homework Example
• Part 4.14 - Calculating Present Value with Multiple Future Cash Flows – Example #2
• Part 4.15 - Valuing Annuity Level Cash Flows – Present & Future Value of Annuities
• Part 4.16 - Calculating Annuity Payments using Annuity Present Value Factor – Example
• Part 4.17 - Accounting for Perpetuities & Using the Annuity Present Value Factor Formula
• Part 4.18 - Accounting for Growing Perpetuities & Simplified Formula for Present Value of Growing Perpetuity - Example of Growing Perpetuity on Rental Cash Flows

From the introduction to time value of money (part 4.1), we can derive a formula, which will be the future value of $1 invested for t periods at a rate of r per period. The equation is:

The expression (1 + r)^t is sometimes referred to as the future value interest factor for $1 invested at r percent for t periods of time.

Let’s use this future value formula to derive the original $121 at the end of the 2nd year.

The table below shows the growth of $100 each year at 10% interest. Each year, the interest earned is equal to the beginning amount multiplied by the interest rate (10%). How much of this $161.05 is simple interest, and how much of it is compounding interest? Well $100 x 0.10 = $10 per year, so in 5 years, the total simple interest is 5 years x $10 = $50. Thus, we can calculate the compounding interest by subtracting $161.05 - $150 = $11.05

The above graph shows the growth of $100 from inception at year 1 earning simple interest of $10 (10%) and earning $11 in the 2nd year, thus making the new total compounded earnings to $21 at the end of year 2. This compounding effect continues to year 5 when the money has grown from $100 to $161.05 in Year 5.

Compound Interest Homework Problem

Consider you found an investment that pays 15% annual interest, which sounds fantastic to you! This makes you invest $1000 in to it, how much will you have in 3 years? How much will you have in 7 years? And at the end of 7 years, how much interest will you have earned, and how much of it will be compounding interest?
Note: We recommend you try this problem without looking at the solution below first, however if you get stuck, feel free to take a peak!

You invested $1000 x 15% = $150 simple interest each year, thus total simple interest in 7 years = $150 x 7 = $1,050