Interest Rates: Types, Determinants, and Applications

TAKEAWAYS:

• Interest rates are the price of money—they reflect the cost of borrowing and the return on lending, influenced by supply/demand, inflation, and central bank policies.
• Nominal vs. real rates: Nominal rates include inflation; real rates adjust for it using the formula $\text{Real Rate}=\text{Nominal Rate}-\text{Inflation}$.
• Effective Annual Rate (EAR) accounts for compounding, making it critical for comparing loans or investments (e.g., Ncell’s mobile loan vs. a bank’s fixed deposit).
• Risk and term structure: Higher risk (e.g., NEPSE stocks) or longer terms (e.g., 10-year government bonds) demand higher interest rates.
• Floating vs. fixed rates: Floating rates (e.g., Daraz’s supplier financing) adjust with market conditions; fixed rates (e.g., NMB Bank loans) offer stability.
• Real-world impact: Interest rates drive loan affordability (e.g., eSewa’s 12% personal loan), investment returns (e.g., NEPSE dividends), and even government borrowing costs (e.g., Nepal Rastra Bank’s repo rate).

1. What Are Interest Rates?

Interest rates are the compensation paid for the use of money over time. They serve three key functions:

1. Incentivize saving: Banks pay interest on deposits (e.g., NMB’s 6% fixed deposit).
2. Discourage excessive borrowing: High rates (e.g., 15% on credit cards) deter over-leveraging.
3. Signal economic conditions: Rising rates (e.g., NRB’s repo rate hike) often indicate inflation concerns.

How Interest Rates Work: The Supply-Demand Model

pie
    title Interest Rate Determination
    "Demand for loans" : 30
    "Supply of savings" : 30
    "Inflation expectations" : 20
    "Central bank policy (NRB)" : 20

• Demand for loans: Businesses (e.g., Daraz suppliers) and individuals (e.g., homebuyers) borrow when rates are low.
• Supply of savings: Households and institutions (e.g., insurance companies) lend when returns are attractive.
• Inflation: Lenders demand higher rates to compensate for eroding purchasing power (e.g., if inflation is 8%, a nominal 10% loan yields a real 2% return).
• Central bank policy: Nepal Rastra Bank (NRB) adjusts the repo rate (currently ~7.5%) to control money supply and inflation.

2. Types of Interest Rates

A. Nominal vs. Real Interest Rates

Why it matters:

• A nominal 10% loan in high-inflation Nepal (e.g., 2023’s 8.5%) yields a real -1.5% return—you lose money!
• Banks and investors always compare real rates when evaluating opportunities.

B. Fixed vs. Floating Rates

Real-world tie-in:

• Pathao drivers often take floating-rate loans (tied to NRB’s policy rate). If NRB cuts rates, their loan costs drop—but if rates rise, their income may not keep up.

3. Determinants of Interest Rates

A. Economic Factors

1. Inflation: Higher inflation → higher nominal rates (lenders demand compensation).
   • Example: In 2022, Nepal’s inflation hit 8.5%; NRB raised the repo rate to 7.5%.
2. GDP Growth: Strong growth increases demand for loans → higher rates.
3. Government Borrowing: If the government issues more bonds (e.g., to fund infrastructure), it competes with private borrowers, pushing rates up.

B. Risk Factors

• Default Risk: Higher for riskier borrowers (e.g., startups vs. NTC).
  • Example: NEPSE-listed companies with low credit ratings pay higher interest on bonds.
• Liquidity Risk: Illiquid assets (e.g., real estate) require higher yields to attract investors.
• Maturity Risk: Longer-term loans (e.g., 20-year mortgages) have higher rates than short-term ones.

C. Central Bank Policy

• Repo Rate: NRB’s benchmark rate (currently ~7.5%). Banks borrow from NRB at this rate.
• Open Market Operations: NRB buys/sells government securities to adjust money supply.
• Reserve Requirements: Higher reserves reduce lending capacity → tighter money supply → higher rates.

4. The Term Structure of Interest Rates

The yield curve shows how interest rates vary with maturity. Three common shapes:

graph LR
    A["Normal (Upward-Sloping)"] -->|"Economic expansion"| B["Short-term < Long-term"]
    C["Inverted (Downward-Sloping)"] -->|"Recession warning"| D["Short-term > Long-term"]
    E["Flat"] -->|"Stagnation"| F["Short-term ≈ Long-term"]

• Normal Curve: Short-term rates < long-term rates (e.g., 6-month T-bill = 6%; 10-year bond = 8%).
• Inverted Curve: Rare in Nepal but seen globally before recessions (e.g., US 2000, 2006).
• Flat Curve: Indicates uncertainty (e.g., post-earthquake Nepal in 2015).

Nepali Example:

• In 2023, Nepal’s 1-year bond yield was ~7%, while the 10-year bond yield was ~9% (normal curve), reflecting growth expectations.

5. Interest Rates in Real-World Finance

A. Loans and Borrowing

1. Personal Loans (e.g., eSewa, NMB Bank)

   • Nominal Rate: 12–24% p.a. (compounded monthly).
   • Real Rate: If inflation = 8%, real cost = 4–16%.
   • EAR Calculation: For a 15% p.a. loan compounded monthly: $$\text{EAR}={\left(1+\frac{0.15}{12}\right)}^{12}-1=15.93\%$$
   • Why? Borrowers pay 15.93% effectively, not 15%.

2. Home Loans (e.g., Global IME, NMB)

   • Fixed rate: 9–12% for 15–20 years.
   • Floating rate: Repo rate + 3% (e.g., 7.5% + 3% = 10.5%).
   • Example: A ₹5,00,000 loan at 10% for 15 years → EMI = ₹4,774/month.

B. Investments and Savings

1. Fixed Deposits (e.g., NMB, Siddhartha Bank)

   • 6–9% p.a. (compounded annually).
   • Example: ₹1,00,000 for 1 year at 8% → ₹1,08,000.

2. Bonds (e.g., Nepal Rastra Bank Bonds, NEPSE-listed)

   • Government bonds: 7–9% (low risk).
   • Corporate bonds: 10–14% (higher risk, e.g., NEPSE-listed cement companies).

C. Stock Market (NEPSE)

• Dividend Yield: Not an interest rate, but related to return.
  • Example: If a stock costs ₹100 and pays ₹5 dividend, yield = 5%.
• Cost of Capital: Companies borrow at ~10–12% (from banks) and expect higher returns on projects.

6. Worked Example: Calculating Loan Costs for a Kathmandu Retail Shop

Scenario: Mr. Thapa runs a grocery shop in Kathmandu. He needs ₹2,00,000 to expand. Two loan options:

1. Fixed Rate: 10% p.a. for 3 years (compounded annually).
2. Floating Rate: Repo rate (7.5%) + 2% = 9.5% p.a., reset every 6 months.

Calculations:

Option 1: Fixed Rate Loan

• Annual Interest: ₹2,00,000 × 10% = ₹20,000.
• Total Repayment: ₹2,00,000 + (₹20,000 × 3) = ₹2,60,000.
• EMI (if monthly): Use the formula $\text{EMI}=P\times \frac{r(1+r{)}^n}{(1+r{)}^n-1}$, where $r=\frac{10\%}{12}=0.83\%$, $n=36$. $$\text{EMI}=200,000\times \frac{0.0083(1.0083{)}^{36}}{(1.0083{)}^{36}-1}=₹6,260/\text{month}$$

Option 2: Floating Rate Loan (First 6 Months)

• First 6 Months Rate: 9.5% p.a. → 4.75% for 6 months.
• Interest: ₹2,00,000 × 4.75% = ₹9,500.
• Principal Repaid: ₹2,00,000 – ₹9,500 = ₹1,90,500 (if paid in full after 6 months).
• New Loan Amount: ₹1,90,500 (rate resets to new repo rate + 2%).

Comparison:

Real-World Decision:

• If Mr. Thapa expects NRB to cut rates in 6 months, floating is cheaper.
• If rates rise, he’d pay more (e.g., if repo goes to 9%, his rate becomes 11%).

7. Interest Rates and Financial Markets

A. Nepal Rastra Bank (NRB) and Monetary Policy

• Tools NRB Uses:
  • Repo Rate: Currently ~7.5% (last hike: June 2023).
  • Bank Rate: 8% (penalty rate for banks borrowing from NRB).
  • Statutory Liquidity Ratio (SLR): 100% (banks must hold 100% of deposits in liquid assets).
• Impact of Rate Hikes:
  • Borrowing becomes expensive (e.g., home loans rise from 9% to 11%).
  • Savings become more attractive (e.g., FD rates rise from 6% to 7%).

B. NEPSE and Stock Valuation

• Cost of Equity: Higher interest rates → higher cost of capital → lower stock valuations.
  • Example: If NRB raises rates, NEPSE’s P/E ratios may drop as investors demand higher returns.
• Bond Prices: Inverse relationship with interest rates.
  • Example: If bond yields rise from 8% to 9%, existing 8% bonds lose value.

8. Common Mistakes to Avoid

1. Ignoring Compounding: Assuming a 12% loan is simple interest when it’s compounded monthly (EAR = 12.68%).
2. Mixing Nominal and Real Rates: Comparing a 10% nominal loan to a 5% real investment without adjusting for inflation.
3. Overlooking Fees: Banks charge processing fees (e.g., 1–2% of loan amount), increasing the true cost.
4. Assuming Fixed Rates Stay Fixed: Some loans have "teaser rates" (e.g., 6% for 1 year, then 12%).

9. In the Real World

1. eSewa Loans

   • Idea Used: Effective Annual Rate (EAR) and risk-based pricing.
   • How? eSewa offers instant loans at 12–24% p.a., compounded monthly. A borrower sees "12% p.a." but pays 12.68% EAR. High-risk borrowers (e.g., those with poor repayment history) get charged higher rates.

2. Nepal Rastra Bank (NRB) Repo Rate

   • Idea Used: Central bank policy and transmission mechanism.
   • How? When NRB raises the repo rate (e.g., from 6% to 7.5%), commercial banks increase their lending rates. This directly affects:
     • Home loan EMIs (rise by ~0.5–1%).
     • Business loans (suppliers to Daraz/Nepal Basket pay more).
     • Government borrowing costs (Nepal issues more bonds at higher yields).

3. NEPSE Stock Valuation

   • Idea Used: Discounted Cash Flow (DCF) and cost of capital.
   • How? Companies like NMB Bank or Himalayan Bank are valued using DCF, where the discount rate includes:
     • Risk-free rate (e.g., 7% from government bonds).
     • Risk premium (e.g., 3–5% for bank stocks).
     • If NRB raises rates, the discount rate increases → lower stock valuations.

10. Exam Tip

What Examiners Look For

1. Definitions:

   • Clearly distinguish between nominal, real, and effective rates.
   • Explain fixed vs. floating rates with examples (e.g., NMB vs. Daraz loans).

2. Calculations:

   • Always show work for EAR, real rate adjustments, and loan EMIs.
   • Example: If asked to compare two loans, calculate both nominal and EAR.

3. Real-World Application:

   • Link concepts to NRB policies, NEPSE stocks, or eSewa loans.
   • Example: "If NRB cuts the repo rate, how would it affect:
     • A) A floating-rate home loan?
     • B) The dividend yield of NEPSE stocks?"

4. Diagrams:

   • Draw the yield curve (normal/inverted/flat) and label axes.
   • Use T-accounts to show how interest expenses affect a company’s equity (e.g., NMB Bank’s interest expense vs. interest income).

5. Common Pitfalls:

   • Don’t confuse simple and compound interest. Always specify compounding frequency.
   • Adjust for inflation when comparing real vs. nominal rates.
   • Mention Nepal-specific examples (e.g., NRB repo rate, NEPSE, eSewa) to score higher.

Sample Exam Questions and Answers

Question 1: "Explain why a borrower might prefer a floating-rate loan over a fixed-rate loan in Nepal’s current economic scenario (2023)."

Answer:

• Scenario: NRB has been raising rates to control inflation (8.5% in 2023).
• Floating Rate Advantage:
  • If NRB cuts rates in the future (e.g., due to slowing growth), the borrower’s loan cost decreases.
  • Example: A floating loan at repo + 2% (currently 9.5%) could drop to 8.5% + 2% = 10.5% if repo falls to 8.5%.
• Risk: If rates rise further, payments increase (e.g., repo at 9% → loan rate = 11%).
• Best For: Borrowers who expect rate cuts (e.g., Pathao drivers, small businesses).

Question 2: "Calculate the Effective Annual Rate (EAR) for a loan offering 12% p.a. compounded quarterly."

Answer: $$\text{EAR}={\left(1+\frac{0.12}{4}\right)}^4-1=(1+0.03{)}^4-1=1.1255-1=12.55\%$$ Visual:

Loan Terms:
- Nominal Rate: 12%
- Compounding: Quarterly (4 times/year)
EAR Calculation:
(1 + 12%/4)^4 - 1 = 12.55%

Why It Matters: The borrower pays 12.55%, not 12%, due to quarterly compounding.

11. Key Formulas to Memorize

12. Summary Table: Interest Rate Types

13. Final Worked Example: Comparing Investments

Scenario: You have ₹50,000 to invest for 3 years. Two options:

1. Fixed Deposit (NMB Bank): 8% p.a., compounded annually.
2. NEPSE Stock (NMB Bank): Expected return = 12% p.a., but volatile.

Calculations:

Option 1: Fixed Deposit

$$\text{FV}=50,000\times (1+0.08{)}^3=50,000\times 1.2597=₹62,985$$

Option 2: NEPSE Stock

• Nominal Return: 12% p.a.
• Real Return: If inflation = 8%, real return = 4% p.a.
• FV (Nominal): $50,000\times (1.12{)}^3=₹70,668$
• FV (Real): $50,000\times (1.04{)}^3=₹58,154$

Decision:

• Safe Investor: Choose FD (guaranteed ₹62,985).
• Risk-Tolerant Investor: Choose stock (higher nominal return but volatile).

Real-World Tie-In:

• In 2023, NEPSE’s real return was negative for many stocks due to high inflation (8.5%), while FDs offered real returns of ~0% (8% nominal – 8.5% inflation).

14. Visual Summary: The Accounting Cycle of Interest

flowchart TD
    A["Start: Borrower/Investor"] --> B["Choose Loan/Investment"]
    B --> C["Fixed or Floating Rate?"]
    C -->|"Fixed"| D["Lock in Rate (e.g., 10%)"]
    C -->|"Floating"| E["Rate Tied to Benchmark (e.g., Repo + 2%)"]
    D --> F["Calculate EMI/FV Using Fixed Rate"]
    E --> G["Monitor NRB Policy for Rate Changes"]
    F --> H["Repay Loan or Realize Returns"]
    G --> H
    H --> I["End: Impact on Cash Flow/Wealth"]