Compound Interest
- A man buys a scooter on making a cash down payment of ₹ 16224 and promises to pay two more yearly instalments of equivalent amount in next two years. If the rate of interest is 4% per annum, compounded yearly, the cash value of the scooter, is
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Let principal (present worth) for first year be P1 and that for two years be P2.
∴ 16224 = P1 
1 + 4 
100 ⇒ 16224 = P1 1 + 1 = 26P1 25 25 ⇒ P1 = 16224 × 25 = ₹ 15600 26
Again,16224 = P2 1 + 4 2 100
Correct Option: B
Let principal (present worth) for first year be P1 and that for two years be P2.
∴ 16224 = P1 1 + 4 100 ⇒ 16224 = P1 1 + 1 = 26P1 25 25 ⇒ P1 = 16224 × 25 = ₹ 15600 26
Again,16224 = P2 1 + 4 2 100 ⇒ 16224 = P2 26 2 = 676P2 25 625 ⇒ P2 = 16224 × 625 = ₹ 15000 676
∴ Cash value of the scooter = ₹ (16224 + 15600 + 15000) = ₹ 46824
- A builder borrows ₹ 2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be ?
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Here , A = ₹ 2550 , R = 4% per annum , n = 2 years
Let each of the two equal instalments be y .Present worth = Instalment 1 + r 
n 100 P1 = y 1 + 4 1 100 P1 = y 1 + 1 25 = y 26 25 or P1 = 25 y 26
Similarly,P2 = 25 2 y = 625 y 26 676
P1 + P2 = A∴ 25 y + 625 y = 2550 26 676 ⇒ (650 + 625)y = 2550 676 ⇒ 1275 y = 2550 676 ⇒ y = 2550 × 676 = ₹ 1352 1275
Second Method to solve this question :
Here, P = ₹ 2550, n = 2, r = 4%Each instalment = P 100 + 100 2 100 + r 100 + r = 2550 100 + 100 2 100 + 4 100 + 4 = 2550 100 + 100 2 104 104
Correct Option: A
Here , A = ₹ 2550 , R = 4% per annum , n = 2 years
Let each of the two equal instalments be y .Present worth = Instalment 1 + r n 100 P1 = y 1 + 4 1 100 P1 = y 1 + 1 25 = y 26 25 or P1 = 25 y 26
Similarly,P2 = 25 2 y = 625 y 26 676
P1 + P2 = A∴ 25 y + 625 y = 2550 26 676 ⇒ (650 + 625)y = 2550 676 ⇒ 1275 y = 2550 676 ⇒ y = 2550 × 676 = ₹ 1352 1275
Second Method to solve this question :
Here, P = ₹ 2550, n = 2, r = 4%Each instalment = P 100 + 100 2 100 + r 100 + r = 2550 100 + 100 2 100 + 4 100 + 4 = 2550 100 + 100 2 104 104 Each instalment = 2550 100 1 + 100 104 104 Each instalment = 2550 100 204 104 104 Each instalment = 2550 × 104 × 104 = ₹ 1352 20400
- A sum of money is invested at 20% compound interest (compounded annually). It would fetch Rs. 723 more in 2 years if interest is compounded half yearly. The sum is
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Let the principal be Rs. P.
When the interest is compounded annually,C.I. = P 
1 + R T − 1 
100 C.I. = P 1 + 20 2 − 1 100 C.I. = P 6 2 − 1 5 C.I. = P 36 − 1 25 C.I. = Rs. 11P 25
When the interest is compounded half–yearly,C.I. = P 1 + 10 4 − 1 100 C.I. = P 11 4 − 1 10 C.I. = P 14641 − 1 10000 C.I. = Rs. 4641P 10000
Correct Option: B
Let the principal be Rs. P.
When the interest is compounded annually,C.I. = P 1 + R T − 1 100 C.I. = P 1 + 20 2 − 1 100 C.I. = P 6 2 − 1 5 C.I. = P 36 − 1 25 C.I. = Rs. 11P 25
When the interest is compounded half–yearly,C.I. = P 1 + 10 4 − 1 100 C.I. = P 11 4 − 1 10 C.I. = P 14641 − 1 10000 C.I. = Rs. 4641P 10000
From the question ,∴ 4641P − 11P = 723 10000 25 ⇒ 4641P − 4400P = 723 10000 ⇒ 241P = 723 10000 ⇒ P = 723 × 10000 = Rs. 30000 241
- The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525 . The simple interest on the same sum for double the time at half the rate percent per annum is :
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Given that , C.I. = Rs. 525 , Time = 2 years , Rate = 10%
Using the given formula ,C.I. = P 1 + R T − 1 100 ⇒ 525 = P 1 + 10 2 − 1 100 ⇒ 525 = P 121 − 1 100 ⇒ 525 = P × 21 100 ⇒ P = 525 × 100 = Rs. 2500 21
Again, new rate = 5% per annum
Correct Option: C
Given that , C.I. = Rs. 525 , Time = 2 years , Rate = 10%
Using the given formula ,C.I. = P 1 + R T − 1 100 ⇒ 525 = P 1 + 10 2 − 1 100 ⇒ 525 = P 121 − 1 100 ⇒ 525 = P × 21 100 ⇒ P = 525 × 100 = Rs. 2500 21
Again, new rate = 5% per annum∴ S.I. = Principal × Time × Rate 100 S.I. = 2500 × 5 × 4 = Rs. 500 100
- A certain amount grows at an annual interest rate of 12%, compounded monthly. Which of the following equations can be solved to find the number of years, y, that it would take for the investment to increase by a factor of 64 ?
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As per the given in question ,
Here , Rate of interest = 12% per annual = 1% per month and Time = 12y months
Using the given formula ,∴ A = P 1 + R T 100
Correct Option: A
As per the given in question ,
Here , Rate of interest = 12% per annual = 1% per month and Time = 12y months
Using the given formula ,∴ A = P 1 + R T 100 ⇒ 64 = 1 1 + 1 12y 100
⇒ 64 = 1(1.01)12y
