Master the concept of Annuity in CBSE Class 11 Applied Mathematics. Learn to calculate future and present values with solved examples and exercises.
An annuity is a series of equal payments made at regular intervals over a specified period. In real-life, this includes monthly rent payments, insurance premiums, or systematic investment plans (SIPs). The regularity of the payment and the fixed amount are the defining characteristics of an annuity.
Step 1: Identify P = 1000, r = 0.05, n = 3.
Step 2: Apply formula A = 1000 × [(1 + 0.05)³ - 1] / 0.05.
Step 3: Calculate (1.05)³ = 1.157625.
Answer: A = 1000 × 0.157625 / 0.05 = 3152.50
An ordinary annuity involves payments made at the end of each period, whereas an annuity due involves payments at the beginning of each period. The timing of the payment affects the interest accumulation, making annuity due slightly more valuable. These are standard models for retirement planning and loan amortizations.
Step 1: Given Ordinary Annuity = 5000, r = 0.10.
Step 2: Calculate Annuity Due = 5000 × (1 + 0.10).
Step 3: Multiply 5000 × 1.1.
Answer: 5500
The present value of an annuity represents the current worth of a series of future payments, discounted at a specific interest rate. This is essential for determining the lump sum needed today to fund future periodic withdrawals. It is widely used in pension fund calculations and mortgage valuations.
Step 1: P = 2000, r = 0.06, n = 5.
Step 2: PV = 2000 × [1 - (1.06)⁻⁵] / 0.06.
Step 3: (1.06)⁻⁵ ≈ 0.7473. PV = 2000 × (1 - 0.7473) / 0.06.
Answer: 8423.33