Mathematics for FinancePYQ Nov 20Question 1209 of 512
All Questions

An amount is lent at a nominal rate of 4.5%\displaystyle 4.5\% per annum compounded quarterly. What would be the gain in rupees over when compounded annually?

Options

A0.56\displaystyle 0.56
B0.45\displaystyle 0.45
C0.076\displaystyle 0.076
D0.85\displaystyle 0.85
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — 0.076\displaystyle 0.076

All Options:

  • A0.56\displaystyle 0.56
  • B0.45\displaystyle 0.45
  • C0.076\displaystyle 0.076
  • D0.85\displaystyle 0.85

Detailed Solution & Explanation

**Derivation of Gain on Quarterly over Annual Compounding** Given: - Nominal Rate (r\displaystyle r) = 4.5%\displaystyle 4.5\% per annum - Time (t\displaystyle t) = 1\displaystyle 1 year - Let Principal (P\displaystyle P) = Rs. 100\displaystyle \text{Rs. }100 **Step 1: Calculate interest compounded quarterly** - Quarterly rate i=4.5%4=1.125%=0.01125\displaystyle i = \frac{4.5\%}{4} = 1.125\% = 0.01125 - Number of periods n=4\displaystyle n = 4 Aq=P(1+i)n=100(1.01125)4≈100×1.045765=Rs. 104.5765A_q = P(1 + i)^n = 100(1.01125)^4 \approx 100 \times 1.045765 = \text{Rs. }104.5765 Interest compounded quarterly=Aq−P=Rs. 4.5765\text{Interest compounded quarterly} = A_q - P = \text{Rs. }4.5765 **Step 2: Calculate interest compounded annually** Aa=P(1+r)t=100(1+0.045)1=Rs. 104.50A_a = P(1 + r)^t = 100(1 + 0.045)^1 = \text{Rs. }104.50 Interest compounded annually=Rs. 4.50\text{Interest compounded annually} = \text{Rs. }4.50 **Step 3: Calculate gain per Rs. 100 principal** Gain=4.5765−4.50=Rs. 0.0765 (which is approximately Rs. 0.076)\text{Gain} = 4.5765 - 4.50 = \text{Rs. }0.0765 \text{ (which is approximately } \text{Rs. }0.076\text{)} Hence, **Option C** is the correct answer.

More Questions from Mathematics for Finance

A sum of money invested in compounded interest doubles itself in four years. In how many years it becomes 32 times of itself as the same rate of compound interest?

The simple interest on 600\displaystyle 600 for 9 months is 27\displaystyle 27. Find the interest rate.

Miss Liza lent 4,000\displaystyle 4,000 in such a way that some amount was given to Mr. A at 3%\displaystyle 3\% p.a. S.I. and rest amount to was given to B at 5%\displaystyle 5\% p.a. S.I., the annual interest from both is 144\displaystyle 144. Find the amount lent to Mr. A.

A certain sum of money was put at S.I. for 2.5\displaystyle 2.5 years at a certain rate of S.I. p.a. Had it been put at 4%\displaystyle 4\% higher rate, it would have fetched 500\displaystyle 500 more. Find the sum of money.

Rs.1,25,000\displaystyle 1,25,000 is borrowed at compound interest at the rate of 2%\displaystyle 2\% for the 1st year, 3%\displaystyle 3\% for the second year and 4%\displaystyle 4\% for the 3rd year. Find the amount to be paid after 3 years.

If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

Ready to Master Mathematics for Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free