4: Introduction to Time Value of Money (TVM) : Part 3

Calculations to show Simple Interest and Compound Interest

Let's calculate both Simple Interest (SI) and Compound Interest (CI) for an investment with the same values and variables, and we'll also consider withdrawals during the investment period to see how they affect the final amounts.

Variables:

· Principal amount (P) = $10,000

· Annual Interest Rate (R) = 5%

· Time period (T) = 3 years

We'll calculate both SI and CI for each year, and assume there is a withdrawal of $2,000 at the end of each year.

Simple Interest Calculation:

Simple Interest formula: SI = (P * R * T) / 100

Year 1

Principal (P)= $10,000

Interest (SI)= ($10,000 * 5% * 1) / 100 = $500

Withdrawal= $2,000

Balance=$8,500

Year 2

Principal (P)= $8,500

Interest (SI)= ($8,500 * 5% * 1) / 100 = $425

Withdrawal= $2,000

Balance= $6,925

Year 3

Principal (P)= $6,925

Interest (SI)= ($6,925 * 5% * 1) / 100 = $346.25

Withdrawal= $2,000

Balance= $5,271.25

Compound Interest Calculation:

Compound Interest formula: A = P(1 + (R/100))^T

Year 1

Principal (P)=$10,000

Interest (CI)=$500 (Initial)

Withdrawal=$2,000

Balance=$9,500

Year 2

Principal (P)=$9,500

Interest (CI)=$475

Withdrawal=$2,000

Balance= $8,975

Year 3

Principal (P)= $8,975

Interest (CI)=$448.75

Withdrawal=$2,000

Balance=$7,423.75

Explanation:

In the simple interest calculation, the interest is calculated only on the initial principal for each year. After each year, a withdrawal of $2,000 is made, reducing the principal.

In the compound cnterest calculation, interest is calculated on the updated principal for each year. The interest is reinvested and compounds annually. After each year, a withdrawal of $2,000 is made from the updated balance.

Key Takeaways:

Simple interest remains constant for each year, as it's based on the initial principal.

Compound interest varies each year because it's based on the updated principal.

Withdrawals reduce the principal in both cases, but the impact is more significant in the compound interest scenario due to compounding.

In summary, simple interest provides a fixed interest amount each year, while compound interest allows your investment to grow more effectively over time, especially when withdrawals are smaller relative to the principal and interest earned.

Authored By

Seshadri Krishnaswamy Iyengar

Mentor - StockEazy Financials