CA FOUNDATION: QUANTITATIVE APTITUDE · TIME VALUE OF MONEY

Annuity: present value and future value

Annuity regular (end of period): FV = A[(1 + i)^n − 1]/i; PV = A[1 − (1 + i)^−n]/i.

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Worked examples

Example 1 · level 1

Arjun deposits ₹3,000 at the end of every year for 2 years in a recurring scheme earning 10% p.a. compounded annually. Find the future value of this annuity (nearest rupee).

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i = 0.1, n = 2, A = ₹3,000.
(1 + i)^2 = 1.21.
FV = 3,000 × (1.21 − 1) ÷ 0.1 = ₹6,300.

Answer: ₹6,300

Example 2 · level 2

Bansal Steels must pay ₹18,000 at the end of each year for 6 years. At 5% p.a., what is the present value of these payments (nearest rupee)?

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i = 0.05, n = 6, A = ₹18,000.
(1 + i)^-6 = 0.7462.
PV = 18,000 × (1 − 0.7462) ÷ 0.05 = ₹91,362.46.

Answer: ₹91,362.46

Example 3 · level 3

Aarav deposits ₹17,000 at the end of every year for 3 years in a recurring scheme earning 12% p.a. compounded annually. Find the future value of this annuity (nearest rupee).

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i = 0.12, n = 3, A = ₹17,000.
(1 + i)^3 = 1.4049.
FV = 17,000 × (1.4049 − 1) ÷ 0.12 = ₹57,364.8.

Answer: ₹57,364.8