Reinvestment Calculator

What is Reinvestment?

Reinvestment is the process of using returns from an investment to purchase additional shares or units of the same or a different investment. This strategy allows investors to take advantage of compound interest, potentially accelerating the growth of their investment over time.

The Compound Interest Formula

The formula for calculating compound interest, which is the basis for reinvestment calculations, is:

\[A = P(1 + \frac{r}{n})^{nt}\]

Where:

• \(A\) = Final amount
• \(P\) = Principal amount (initial investment)
• \(r\) = Annual interest rate (in decimal form)
• \(n\) = Number of times interest is compounded per year
• \(t\) = Number of years

Step-by-Step Reinvestment Calculation

1. Determine the principal amount (P), annual interest rate (r), compounding frequency (n), and investment term (t).
2. Convert the annual interest rate to decimal form (divide by 100).
3. Divide the annual rate by the compounding frequency to get the periodic rate.
4. Multiply the compounding frequency by the number of years to get the total number of compounding periods.
5. Apply these values to the compound interest formula.
6. Calculate the final amount (A).
7. Subtract the principal from the final amount to determine the interest earned.

Example Calculation

Let's calculate the reinvestment returns for an initial investment of $10,000, with an annual interest rate of 7%, compounded monthly, over 10 years:

1. \(P = \$10,000\), \(r = 7\% = 0.07\), \(n = 12\) (monthly compounding), \(t = 10\) years
2. Periodic rate = \(0.07 \div 12 = 0.005833\)
3. Total compounding periods = \(12 \times 10 = 120\)
4. \(A = 10000(1 + 0.005833)^{120} = \$20,097.57\)
5. Interest earned = \$20,097.57 - \$10,000 = \$10,097.57

Visual Representation

The green portion represents the principal ($10,000), and the blue portion represents the interest earned through reinvestment ($10,097.57).