Financial Mathematics - Calculation of Interest & Annuities | PAPER III – ACCOUNTING & FINANCIAL MANAGEMENT FOR BANKERS | MODULE C: FINANCIAL MANAGEMENT
Financial Mathematics – Calculation of Interest & Annuities
What is Simple Interest?
Simple Interest is calculated only on the original principal amount over the period of investment or loan. The formula is:
SI = (P × R × T) / 100
Where:
- P = Principal
- R = Rate of Interest per annum
- T = Time in years
Example: If ₹10,000 is invested at 5% per annum for 3 years, then SI = (10000×5×3)/100 = ₹1,500.
What is Compound Interest?
Compound Interest is calculated on the principal plus accumulated interest. The formula is:
CI = P × (1 + R/100)T – P
Example: For ₹10,000 at 5% p.a. compounded annually for 3 years:
CI = 10000 × (1.05)3 – 10000 = ₹1,576.25
Fixed and Floating Interest Rates
Fixed Rate: Remains constant over the loan/investment term.
Floating Rate: Varies based on market benchmark rates such as repo rate or MCLR.
Front-end and Back-end Interest Rates
Front-end: Interest is charged at the beginning of the loan period, reducing disbursal amount.
Back-end: Interest is added at the end, increasing repayment burden over time.
Interest Calculation Using Products/Balances
This method uses the number of days and balances maintained. Product = Balance × No. of days. Interest is:
Interest = (Total Products × Rate) / (100 × 365)
What are Annuities?
An annuity is a series of equal payments made at regular intervals. Types:
- Ordinary Annuity: Payments at end of each period
- Annuity Due: Payments at beginning of each period
Future Value of an Ordinary Annuity (FVOA)
FVOA = A × [(1 + r)n – 1] / r
Where A = annuity amount, r = interest rate per period, n = number of periods
Present Value of an Ordinary Annuity (PVOA)
PVOA = A × [1 – (1 + r)–n] / r
Future Value of an Annuity Due (FVAD)
FVAD = FVOA × (1 + r)
Present Value of an Annuity Due (PVAD)
PVAD = PVOA × (1 + r)
Repayment of a Debt
Debt repayment using annuities involves finding the fixed periodic payment that will amortize the loan. Formula:
EMI = P × r × (1 + r)n / [(1 + r)n – 1]
Mathematical Examples
- Calculate SI for ₹8,000 at 6% for 4 years: SI = (8000×6×4)/100 = ₹1,920
- CI for ₹5,000 at 10% p.a. compounded annually for 2 years: CI = 5000×(1.1)2 – 5000 = ₹1,050
- FVOA for ₹1,000 monthly at 8% p.a. (0.667% monthly) for 12 months:
FVOA = 1000×[(1 + 0.00667)12 – 1]/0.00667 ≈ ₹12,728.27 - PVOA for ₹2,000 monthly at 6% p.a. (0.5% monthly) for 10 months:
PVOA = 2000×[1 – (1.005)–10]/0.005 ≈ ₹19,519.91 - EMI on loan of ₹1,00,000 at 12% p.a. for 12 months (r = 1% monthly):
EMI = 100000×0.01×(1.01)12 / [(1.01)12 – 1] ≈ ₹8,885.52
MCQs
- What is the formula for Simple Interest?
A. P×R×T
B. (P×R×T)/100
C. P×R/T
D. (P+R+T)/100
Answer: B - Which type of interest is calculated on principal and accumulated interest?
A. Simple Interest
B. Nominal Interest
C. Compound Interest
D. Real Interest
Answer: C - Floating interest rate varies with:
A. Inflation
B. Time
C. Market benchmark
D. Loan tenure
Answer: C - Which formula calculates EMI?
A. P × r × T
B. A × (1 + r)n
C. P × r × (1 + r)n / [(1 + r)n – 1]
D. P × T / r
Answer: C - In an annuity due, payments are made:
A. Quarterly
B. End of each period
C. Randomly
D. Beginning of each period
Answer: D - Which of the following is used to calculate compound interest?
A. P × T × R / 100
B. P × (1 + R/100)T – P
C. P + R + T
D. P × R / T
Answer: B - FV of an ordinary annuity is calculated using:
A. A × [(1 + r)n – 1] / r
B. A / (1 + r)n
C. A × (1 – r)n
D. A × r / (1 + r)n
Answer: A - Which method uses product of balance and time for interest calculation?
A. EMI Method
B. Product Method
C. Declining Balance
D. Annuity Method
Answer: B - The present value of an annuity due is calculated by:
A. PVOA × (1 + r)
B. FVOA / (1 + r)
C. PVAD × (1 – r)
D. None of the above
Answer: A - Which is a front-end interest feature?
A. Interest added at repayment
B. Interest charged during loan tenure
C. Interest deducted before loan disbursal
D. Interest paid after loan closes
Answer: C
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