Simple & Compound Interest

Learning Objective: Calculate simple and compound interest for financial scenarios

When you deposit money in a bank in Nepal, the bank pays you extra money called interest for letting them use your savings. When you borrow money for a business, you pay interest to the lender. Understanding how interest is calculated -- whether simple or compound -- is essential for making smart financial decisions.

Simple Interest (SI)

In simple interest, the interest is calculated only on the original principal (the initial amount) for each period.

Formula: SI = P x R x T / 100

Where:

• P = Principal (initial amount)
• R = Rate of interest per year (%)
• T = Time (in years)

Amount = P + SI

Worked Example 1

Ram deposits Rs. 50,000 in a savings account at Nepal Bank at 6% per year for 3 years.

SI = 50,000 x 6 x 3 / 100 = Rs. 9,000

Amount = 50,000 + 9,000 = Rs. 59,000

Ram earns Rs. 9,000 in interest over 3 years.

Worked Example 2

Sita borrows Rs. 1,00,000 from a microfinance institution at 12% per year for 2 years.

SI = 1,00,000 x 12 x 2 / 100 = Rs. 24,000

She must repay: 1,00,000 + 24,000 = Rs. 1,24,000

Compound Interest (CI)

In compound interest, the interest is calculated on the principal plus previously earned interest. This means you earn "interest on interest," making your money grow faster.

Formula: A = P (1 + R/100)^T

CI = A - P

Where:

• A = Final amount
• P = Principal
• R = Rate of interest per year (%)
• T = Time (in years)

Worked Example 3

Hari deposits Rs. 50,000 in a fixed deposit at NIC Asia Bank at 8% compound interest for 3 years.

A = 50,000 x (1 + 8/100)^3 A = 50,000 x (1.08)^3 A = 50,000 x 1.2597 A = Rs. 62,985

CI = 62,985 - 50,000 = Rs. 12,985

Compare this with simple interest at the same rate: SI = 50,000 x 8 x 3 / 100 = Rs. 12,000

Compound interest earns Rs. 985 more than simple interest over 3 years!

SI vs. CI Comparison

| Feature | Simple Interest | Compound Interest | |---------|----------------|-------------------| | Interest on | Principal only | Principal + accumulated interest | | Growth | Linear (same each year) | Exponential (grows faster) | | Formula | P x R x T / 100 | P(1 + R/100)^T - P | | Better for | Borrowers (pay less) | Savers (earn more) |

Annuities Basics

An annuity is a series of equal payments made at regular intervals. Common examples:

• Monthly installment payments on a motorcycle loan
• Monthly SIP (Systematic Investment Plan) in mutual funds
• Monthly pension payments after retirement

Example: If you invest Rs. 2,000 per month in a mutual fund at 10% annual return, after 10 years the investment grows substantially due to regular contributions plus compound growth.

Key Term: Compound Interest calculates interest on both the original principal and the accumulated interest from previous periods, causing savings to grow exponentially over time.

Summary

• Simple interest is calculated on the principal only: SI = P x R x T / 100.
• Compound interest is calculated on principal plus earned interest: A = P(1 + R/100)^T.
• Compound interest always yields more than simple interest over the same period.
• Annuities involve regular equal payments, useful for loans and investments.