Future and Present Value of Ordinary Annuity and Annuity Due (up to 3 periods)

1

easyIf P = 100, i = 0.1, n = 1, the Future Value of an Ordinary Annuity is:

A. 100 B. 110 C. 121 D. 133.1

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✔ Correct: A

FV = 100 × [(1.1)¹ − 1] / 0.1 = 100 × 0.1 / 0.1 = 100.

2

easyFor P = 200, i = 0.05, n = 2, the Present Value of an Ordinary Annuity is:

A. 371.88 B. 400 C. 380.95 D. 410.50

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✔ Correct: A

PV = 200 × [1 − (1.05)⁻²] / 0.05 = 200 × [1 − 0.9070] / 0.05 = 371.88.

3

mediumCalculate the Future Value of an Annuity Due for P = 1000, i = 0.1, n = 2.

A. 2100 B. 2200 C. 2310 D. 2420

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✔ Correct: C

FV_due = 1000 × [(1.1)² − 1] / 0.1 × 1.1 = 1000 × 2.1 × 1.1 = 2310.

4

mediumIf PV = 2725, i = 0.1, n = 3, find the annual payment P for an Ordinary Annuity.

A. 1000 B. 1050 C. 1100 D. 1200

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✔ Correct: C

2725 = P × [1 − (1.1)⁻³] / 0.1 = P × 2.4868. P = 2725 / 2.4868 ≈ 1100.

5

hardCompare FV of Ordinary Annuity vs Annuity Due for P = 100, i = 0.1, n = 3. Difference is:

A. 31 B. 33.1 C. 36.41 D. 10

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✔ Correct: B

FV_ord = 100 �� (1.331 − 1) / 0.1 = 331. FV_due = 331 × 1.1 = 364.1. Difference = 33.1.

6

hardFind the Present Value of an Annuity Due for P = 500, i = 0.1, n = 2.

A. 909.09 B. 954.54 C. 1000 D. 867.76

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✔ Correct: B

PV_due = PV_ord × (1 + i) = 500 × [1 − (1.1)⁻²] / 0.1 × 1.1 = 500 × 1.7355 × 1.1 = 954.54.

7

very hardIf the Present Value of an Ordinary Annuity for 3 years is 2486.8 and i = 0.1, what is the payment P?

A. 800 B. 900 C. 1000 D. 1200

Show Answer

✔ Correct: C

2486.8 = P × [1 − (1.1)⁻³] / 0.1. 2486.8 = P × 2.4868. P = 1000.

1

Assertion (A): The Future Value of an Annuity Due is always greater than an Ordinary Annuity for the same P, i, and n.
Reason (R): Annuity Due payments are made at the start of the period, allowing each payment to earn interest for one additional period.

Choose the correct option:
(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true but R is not the correct explanation of A.
(C) A is true but R is false.
(D) A is false but R is true.

A. Option A B. Option B C. Option C D. Option D

Show Answer

✔ Correct: A

Both assertion and reason are true, and the reason correctly explains the assertion.

2

Assertion (A): For n=1, the Present Value of an Ordinary Annuity and Annuity Due are identical.
Reason (R): At n=1, the payment is made at the end of the period for both types, thus discounting is identical.

Choose the correct option:
(A) Both A and R are true and R is the correct explanation of A.
(B) Both A and R are true but R is not the correct explanation of A.
(C) A is true but R is false.
(D) A is false but R is true.

A. Option A B. Option B C. Option C D. Option D

Show Answer

✔ Correct: C

Assertion is true, but reason is false because Annuity Due payments are at the start, making PV_due = P/(1+i) and PV_ord = P/(1+i), but the timing definition differs.

1

mediumGiven P = 2000, i = 0.1, n = 3. Find: (i) FV of Ordinary Annuity (ii) PV of Ordinary Annuity (iii) FV of Annuity Due.

Show Answer & Solution

(i) 2000 × (1.331 − 1) / 0.1 = 6620.
(ii) 2000 × (1 − 0.7513) / 0.1 = 4974.
(iii) 6620 × 1.1 = 7282.

2

mediumGiven P = 500, i = 0.05, n = 2. Find: (i) FV of Ordinary Annuity (ii) PV of Ordinary Annuity (iii) PV of Annuity Due.

Show Answer & Solution

(i) 500 × (1.1025 − 1) / 0.05 = 1025.
(ii) 500 × (1 − 0.9070) / 0.05 = 930.
(iii) 930 × 1.05 = 976.5.

3

hardGiven P = 1000, i = 0.2, n = 3. Find: (i) FV of Ordinary Annuity (ii) PV of Ordinary Annuity (iii) Difference between FV_due and FV_ord.

Show Answer & Solution

(i) 1000 × (1.728 − 1) / 0.2 = 3640.
(ii) 1000 × (1 − 0.5787) / 0.2 = 2106.5.
(iii) 3640 × 0.2 = 728.

1

hardA person deposits ₹5000 at the end of each year for 3 years at 10% interest compounded annually. Calculate the total amount accumulated and the present value of these payments.

Show Answer & Solution

Step 1: Identify P=5000, i=0.1, n=3.
Step 2: FV = 5000 × [(1.1)³ − 1] / 0.1.
Step 3: FV = 5000 × 0.331 / 0.1 = 16550.
Step 4: PV = 5000 × [1 − (1.1)⁻³] / 0.1.
Step 5: PV = 5000 × 2.4868 = 12434.

2

very hardCompare the Future Value of an investment of ₹10000 for 3 years at 10% interest if payments are made at the start of the year vs end of the year.

Show Answer & Solution

Step 1: Ordinary Annuity (End): FV = 10000 × [(1.1)³ − 1] / 0.1.
Step 2: FV = 10000 × 3.31 = 33100.
Step 3: Annuity Due (Start): FV = 33100 × 1.1.
Step 4: FV_due = 36410.
Step 5: The difference is 36410 − 33100 = 3310.

★

Case Study: A small business invests ₹20000 at the end of each year for 3 years in a fund yielding 10% interest. The business also considers an alternative plan of investing at the start of the year.

Sub-question 1: (i) Calculate the Future Value of the end-of-year investment plan.

Show Solution

FV = 20000 × [(1.1)³ − 1] / 0.1 = 20000 × 3.31 = 66200.

Sub-question 2: (ii) Calculate the Future Value of the start-of-year investment plan.

Show Solution

FV_due = 66200 × 1.1 = 72820.

Ordinary Annuity: Future Value

Ordinary Annuity: Present Value

Annuity Due: Future Value

Section A: Multiple Choice Questions (MCQs)

Section B: Assertion–Reason Questions

Section C: Short Answer Questions

Section D: Long Answer Questions

Section E: Case-Based Question

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