Question 1
If the difference between the annually compounded interest and simple interest on a certain sum of money at 8% per annum for 3 years is Rs. 788, then the principal amount is ______________.
Explanation
For 3 years, CI - SI = P × [(1+r)3 - 1 - 3r], where r = 0.08.
(1.08)3 = 1.259712, so (1.08)3 - 1 - 3(0.08) = 1.259712 - 1 - 0.24 = 0.019712.
P = 7880.019712 ≈ Rs. 39,975.
(1.08)3 = 1.259712, so (1.08)3 - 1 - 3(0.08) = 1.259712 - 1 - 0.24 = 0.019712.
P = 7880.019712 ≈ Rs. 39,975.
Question 2
A machine depreciates at a rate of 10% per year on its beginning-of-year value. If it is sold for Rs. 6,000 after 9 years, what was its original purchase price?
Explanation
Value after 9 years = Original Price × (0.9)9, so Original Price = 6,000(0.9)9.
(0.9)9 ≈ 0.38742, so Original Price = 6,0000.38742 ≈ Rs. 15,488.
(0.9)9 ≈ 0.38742, so Original Price = 6,0000.38742 ≈ Rs. 15,488.
Question 3
Rakesh requires Rs. 1,00,000 to buy a scooter after 4 years. What will be the approximate present value of Rs. 1,00,000 if the interest rate is 10% per annum?
Explanation
PV = 1,00,000(1.1)4.
(1.1)4 = 1.4641, so PV = 1,00,0001.4641 ≈ Rs. 68,300.
(1.1)4 = 1.4641, so PV = 1,00,0001.4641 ≈ Rs. 68,300.
Question 4
Raju deposits Rs. 20,000 in a nationalized bank for 3 years at an annual interest rate of 8%, with the interest compounded every quarter. Find out how much interest Raju earns in the first year and the second year.
Explanation
Quarterly rate = 2%. Compounding 20,000 for 4 quarters (year 1): 20,000 × (1.02)4 = 20,000 × 1.082432 = 21,648.64.
Interest in year 1 = 21,648.64 - 20,000 = Rs. 1,648.64.
Compounding for 4 more quarters (year 2): 21,648.64 × (1.02)4 = 21,648.64 × 1.082432 ≈ 23,433.19.
Interest in year 2 = 23,433.19 - 21,648.64 ≈ Rs. 1,784.54.
Interest in year 1 = 21,648.64 - 20,000 = Rs. 1,648.64.
Compounding for 4 more quarters (year 2): 21,648.64 × (1.02)4 = 21,648.64 × 1.082432 ≈ 23,433.19.
Interest in year 2 = 23,433.19 - 21,648.64 ≈ Rs. 1,784.54.
Question 5
Find the effective interest rate, if the nominal rate is 12% per annum, quarterly compounding.
Explanation
Effective rate = 1 + 0.1244 - 1 = (1.03)4 - 1.
(1.03)4 = 1.12550881, so effective rate = 0.1255 = 12.55%.
(1.03)4 = 1.12550881, so effective rate = 0.1255 = 12.55%.
Question 6
The compound interest for Rs. 15,000 at 20% per annum for 2 years compounded semi-annually is __________.
Explanation
Semi-annual rate = 10%, number of periods = 4.
Amount = 15,000 × (1.1)4 = 15,000 × 1.4641 = Rs. 21,961.50.
Compound Interest = 21,961.50 - 15,000 = Rs. 6,961.50.
Amount = 15,000 × (1.1)4 = 15,000 × 1.4641 = Rs. 21,961.50.
Compound Interest = 21,961.50 - 15,000 = Rs. 6,961.50.
Question 7
Mr. Amit bought a car for Rs. 3,00,000 by making a down payment of Rs. 50,000 and decided to pay equal annual payments for 10 years. How much would each payment be if the interest on the unpaid amount is 18% per annum, compounded annually? (Given that P(10, 0.18) = 4.49409)
Explanation
Unpaid amount to be financed = 3,00,000 - 50,000 = Rs. 2,50,000.
Annual payment = 2,50,000P(10, 0.18) = 2,50,0004.49409 ≈ Rs. 55,628.61.
Annual payment = 2,50,000P(10, 0.18) = 2,50,0004.49409 ≈ Rs. 55,628.61.
Question 8
The simple interest at the rate of p% per annum for p years will be Rs. p. Then, the principal is ____________.
Explanation
SI = P × r × t100 = P × p × p100 = P p2100. Given this equals p:
P p2100 = p ⇒ P = 100p.
P p2100 = p ⇒ P = 100p.
Question 9
The future value of an annuity of Rs. 2000 made annually for 8 years at interest rate of 14% per annum, compounded annually is _______. (Given that (1.14)8 = 2.8526)
Explanation
FV = P × (1+r)n - 1r = 2000 × 2.8526 - 10.14 = 2000 × 1.85260.14 ≈ 2000 × 13.2329 ≈ Rs. 26,465.71.
Question 10
Ravi deposits some amount in a bank for 512 years at the simple interest rate of 7% per annum. Ravi receives Rs. 66,480 at the end of the term. Compute the amount of the initial deposit by Ravi in the Bank.
Explanation
Amount = P(1 + rt) = P(1 + 0.07 × 5.5) = P(1 + 0.385) = 1.385P.
P = 66,4801.385 = Rs. 48,000.
P = 66,4801.385 = Rs. 48,000.
Question 11
In how many years will Rs. 50,000 become Rs. 75,000 at 8% per annum compound interest? (Given log(1.5) = 0.1761 and log(1.08) = 0.0334)
Explanation
75,00050,000 = 1.5 = (1.08)n.
n = log(1.5)log(1.08) = 0.17610.0334 ≈ 5.27, i.e. about 5.3 years.
n = log(1.5)log(1.08) = 0.17610.0334 ≈ 5.27, i.e. about 5.3 years.
Question 12
A loan of Rs. 1,00,000 is repaid in 3 equal annual instalments at 10% per annum interest, compounded annually. Find the amount of each instalment. (Given P(3, 0.1) = 2.48685)
Explanation
Instalment = 1,00,000P(3, 0.1) = 1,00,0002.48685 ≈ Rs. 40,212.