CA Foundation P3 · Chapter 4
Mathematics of Finance MCQs with Answers
10 multiple-choice questions on Mathematics of Finance for CA Foundation P3 Quantitative Aptitude. Try each one before revealing the answer and explanation.
Practise this chapter interactivelyQuestion 1
The simple interest on ₹12,000 at 8% per annum for 2½ years is:
- A) ₹1,920
- B) ₹14,400
- C) ₹2,400
- D) ₹2,40,000
Show answer & explanation
Answer: C) ₹2,400
SI = P x R x T / 100 = 12,000 x 8 x 2.5 / 100 = ₹2,400. ₹1,920 is the interest for 2 years only, ₹14,400 is the amount (principal plus interest), and ₹2,40,000 results from not dividing by 100.
Question 2
The compound interest on ₹20,000 for 1½ years at 10% per annum compounded half-yearly is:
- A) ₹3,152.50
- B) ₹3,000.00
- C) ₹6,620.00
- D) ₹3,073.79
Show answer & explanation
Answer: A) ₹3,152.50
Half-yearly rate = 10/2 = 5% and number of periods = 1.5 x 2 = 3. Amount = 20,000 x (1.05)³ = 20,000 x 1.157625 = ₹23,152.50, so CI = ₹3,152.50. Simple interest would be ₹3,000; using 10% for 3 periods gives ₹6,620; compounding annually (1.1^1.5) gives about ₹3,073.79.
Question 3
The effective annual rate of interest corresponding to a nominal rate of 12% per annum compounded quarterly is (to two decimals):
- A) 12.00%
- B) 12.55%
- C) 12.36%
- D) 48.00%
Show answer & explanation
Answer: B) 12.55%
Quarterly rate = 12/4 = 3%. Effective rate E = (1 + 0.03)⁴ − 1 = 1.12550881 − 1 = 0.1255, i.e. 12.55% (rounded to two decimals). 12.36% is the effective rate for half-yearly compounding, (1.06)² − 1.
Question 4
The difference between compound interest and simple interest on ₹15,000 for 2 years at 6% per annum (compounded annually) is:
- A) ₹1,800
- B) ₹1,854
- C) ₹54
- D) ₹108
Show answer & explanation
Answer: C) ₹54
For 2 years, CI − SI = P(R/100)² = 15,000 x (0.06)² = 15,000 x 0.0036 = ₹54. Check: CI = 15,000(1.06² − 1) = 15,000 x 0.1236 = ₹1,854 and SI = 15,000 x 0.06 x 2 = ₹1,800; difference ₹54.
Question 5
At what rate of simple interest per annum will a sum double itself in 8 years?
- A) 12.5%
- B) 8%
- C) 9.05%
- D) 16%
Show answer & explanation
Answer: A) 12.5%
A sum doubles when SI = P. So P = P x R x 8 / 100, giving R = 100/8 = 12.5%. The value 9.05% is the compound rate, 2^(1/8) − 1, which applies only if interest is compounded.
Question 6
₹5,000 is deposited at the end of each year for 4 years at 10% per annum compounded annually. The amount at the end of 4 years is:
- A) ₹20,000
- B) ₹15,849.33
- C) ₹25,525.50
- D) ₹23,205
Show answer & explanation
Answer: D) ₹23,205
Future value of an ordinary annuity = A[(1 + i)ⁿ − 1]/i = 5,000 x (1.1⁴ − 1)/0.1 = 5,000 x (1.4641 − 1)/0.1 = 5,000 x 4.641 = ₹23,205. ₹15,849.33 is the present value, ₹25,525.50 is the annuity-due amount (x 1.1), and ₹20,000 ignores interest.
Question 7
The present value of an ordinary annuity of ₹10,000 per annum for 3 years at 8% per annum compounded annually is (to the nearest paisa):
- A) ₹25,770.97
- B) ₹30,000.00
- C) ₹32,464.00
- D) ₹27,832.65
Show answer & explanation
Answer: A) ₹25,770.97
PV = A[1 − (1 + i)^(−n)]/i = 10,000 x [1 − (1.08)^(−3)]/0.08. (1.08)³ = 1.259712, so (1.08)^(−3) = 0.793832 and the factor = 0.206168/0.08 = 2.577097. PV = ₹25,770.97. ₹32,464 is the future value and ₹27,832.65 is the annuity-due present value (x 1.08).
Question 8
A company wants to accumulate ₹5,00,000 in 5 years through equal deposits made at the end of each year into a sinking fund earning 8% per annum compounded annually. The annual deposit (to the nearest paisa) is:
- A) ₹1,00,000.00
- B) ₹1,25,228.23
- C) ₹78,915.03
- D) ₹85,228.23
Show answer & explanation
Answer: D) ₹85,228.23
Sinking fund deposit = FV / [((1 + i)ⁿ − 1)/i]. (1.08)⁵ = 1.469328, so the factor = 0.469328/0.08 = 5.866601. Deposit = 5,00,000 / 5.866601 = ₹85,228.23 (rounded to the paisa). Using the present-value factor 3.992710 instead gives ₹1,25,228.23, and treating deposits as at the beginning of the year gives ₹78,915.03.
Question 9
The present value of a perpetuity of ₹6,000 receivable at the end of every year, when money is worth 12% per annum, is:
- A) ₹72,000
- B) ₹50,000
- C) ₹56,000
- D) ₹5,357
Show answer & explanation
Answer: B) ₹50,000
PV of a perpetuity = A/i = 6,000/0.12 = ₹50,000. ₹56,000 is the value of a perpetuity due (payment also at the start: 50,000 + 6,000), and ₹72,000 results from multiplying by 12 instead of dividing.
Question 10
A loan of ₹1,00,000 is to be repaid in 3 equal annual instalments, the first payable one year after the loan, with interest at 10% per annum compounded annually. Each instalment (to the nearest paisa) is:
- A) ₹33,333.33
- B) ₹43,333.33
- C) ₹40,211.48
- D) ₹36,555.89
Show answer & explanation
Answer: C) ₹40,211.48
Instalment = P / [(1 − (1 + i)^(−n))/i]. (1.1)³ = 1.331, so (1.1)^(−3) = 0.751315 and the factor = 0.248685/0.1 = 2.486852. Instalment = 1,00,000/2.486852 = ₹40,211.48. ₹33,333.33 ignores interest, ₹43,333.33 adds one year's flat interest, and ₹36,555.89 treats the instalments as an annuity due.