Insurance and Annuity — Meaning, Formulas & Solved Examples

NegativeRekt

3 months ago

Insurance and annuity formulas chart with example problems and solutions for students.

Insurance and Annuity — Concepts, Formulas & Examples

Insurance and Annuity are important concepts in financial mathematics. They are widely used in real life for calculating premiums, claims, and regular payments. This guide explains both topics with formulas, solved examples, and real-life applications.

1. What is Insurance?

Insurance is a contract where an individual (policyholder) pays a fixed amount called premium to an insurance company in exchange for financial protection against specific risks. Learn more from the Insurance Regulatory and Development Authority of India.

Important Terms in Insurance

Sum Assured: The amount the company agrees to pay in case of loss.
Premium: The amount paid regularly (monthly, yearly) by the policyholder.
Policy Term: The time period for which the insurance is valid.
Loss: The financial damage suffered by the policyholder.

Insurance Formula

Premium = (Sum Assured × Rate of Premium) / 100

Example 1: A house worth ₹20,00,000 is insured against fire at a rate of 0.5% per year. Find the annual premium.

Solution: Premium = (20,00,000 × 0.5) / 100 = ₹10,000

2. What is Annuity?

An annuity is a series of equal payments made at regular intervals for a fixed number of years. Learn more about annuities on Investopedia.

Types of Annuities

Immediate Annuity: Payments start right away.
Deferred Annuity: Payments start after a certain time period.

Annuity Formulas

(a) Present Value of Annuity (PVA):

PVA = R × [1 - (1 + i)^-n] / i

(b) Future Value of Annuity (FVA):

FVA = R × [(1 + i)ⁿ - 1] / i

Example 2: A scholarship gives ₹5,000 at the end of each year for 4 years at 6% interest. Find the present value.

Solution: PVA = 5000 × [1 – (1.06)^(-4)] / 0.06 ≈ ₹17,325

Example 3: ₹2,000 is deposited every year for 5 years at 8% interest. Find the total amount after 5 years.

Solution: FVA = 2000 × [(1.08)^5 – 1] / 0.08 ≈ ₹11,732.50

3. Key Differences Between Insurance and Annuity

Insurance	Annuity
Protects against a possible loss	Provides steady payments
Premium is paid to get protection	Payments are received regularly

4. Related Topics

5. Real-Life Applications

Calculating insurance premiums for property
Finding scholarship value using annuity formulas
Planning regular savings

FAQs on Insurance and Annuity

Q1. What is the formula for insurance premium?

Premium = (Sum Assured × Rate of Premium) / 100

Q2. How is present value of annuity calculated?

PVA = R × [1 – (1 + i)^-n] / i

Q3. What is the difference between immediate and deferred annuity?

Immediate annuity starts payments right away, deferred starts after a set period.