 # Compound Interest Problems for Bank Po with Solution for SBI PO 2020 and LIC AAO 2020, NIACL at Smartkeeda

Important for :
1
Shantanu borrowed Rs. 2.5 lakh from a bank to purchase one car. If the rate of interest be 6% per annum compounded annually, what payment he will have to make after 2 years 6 months?
» Explain it
D
CI for 2 years 6 months at the rate of 6, applying the net% effect for first 2 years

 = 6 + 6 + 6 × 6 = 12.36% 100

 Rate of interest for 6 months = 6 × 6 = 3% 12

 For next 6 months = 12.36 + 3 + 12.36 × 3 = 15.36 + 0.37%  = 15.73% 100

Here, we can see that in 2 years 6 months the given compound rate of interest is approximate 15.73%.

 Now, 115.73% of 250000 = 115.73 × 250000 = 289,325. 100

Hence, option D is correct.
2
A certain amount of money is lent out at compound interest at the rate of 20% per annum for two years, compounded annually. It would give Rs. 482 more if the amount is compounded half yearly. Find the principle.
» Explain it
E
Approach I:  To solve this question, we can apply the net % effect formula

 x + y + xy % 100
Compounded annually at rate 20% per annum for 2 years, we get
 = 20 + 20 + 20 × 20 = 44% 100

Similarly, compounded half yearly at rate 10%, we get
 = 10 + 10 + 10 × 10 = 21% 100

 And, 21 + 10 + 21 × 10 = 33.1% 100

 And, 33.1 + 10 + 33.1 × 10 = 46.41% 100

Now as per the question,

Difference between compound interest yearly and half yearly = 46.41 – 44 = 2.41%

Given, 2.41% ≡ 482
100% ≡ x
 ⇒ x = 482 × 100 = 20,000 2.41

Approach II:

When compounded annually, the amount received at the end of the period is

 A = P [ 1 + r ] n 100

When compounded half yearly, the amount received at the end of the period is
 A = P [ 1 + r/2 ] 2n 100

Let the principle be P.

Interest on this amount when compounded annually at the rate of 20% per annum = P [(1.20)2 − 1]
Interest on this amount when compounded half yearly = P [(1.10)4 − 1]

The difference between the two is Rs. 482

∴   P [(1.10)4 − 1] – P [(1.20)2 −1] = 482

∴   P [1.4641 – 1.44] = 482

∴   P = Rs. 20,000

Hence, option E is correct.

3
A man gave 50% of his savings of Rs 67,280 to his wife and divided the remaining sum between his two sons A and B of 14 and 12 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was
» Explain it
D
Total Income = 67,280

After giving 50% salary to his wife the man is left with an amount = 33,640

Let's assume the man gave Rs. x to A. Therefore B will get Rs. (33640 – x).

 ↙ 33640 ↘ 14 years A 12 years B x (33640 – x)

Now, as per the question A & B will be getting an equal amount with CI at 5% rate per year at the 18th year.

 ⇒  x ( 1 + 5 ) 4 = (33640 – x) [ 1+ 5 ] 6 100 100

⇒
 x (33640 – x)
=
 ( 1 + 5 ) 6 100

 ( 1 + 5 ) 4 100

 ⇒ x = ( 21 × 21 ) (33640 – x) 20 20

⇒ 400 x = 33640 × 441 – 441x

⇒ 841x = 33640 × 441

 x = 33640 × 441 = 40 × 441 = 17640/- 841

Therefore, at the time of divison of money, B would have got a sum = (33640 – 17640) = Rs. 16000

Hence, option D is correct.
4
Aditya and Bhushan invested 10000 each in scheme A and scheme B respectively for 3 years. Scheme A offers Simple interest @ 12% per annum and scheme B offers compound interest @ 10%. After 3 years, who will have larger amount and by how much?
» Explain it
C
Lets first calculate the total rate % that Aditya will have after 3 years:

As per the question Aditya invested at rate of 12% pa simple interst

So, for 3 years tenure he will get = 12 × 3 = 36%

And the amount that Bhushan invested at rate of 10% pa compound interest

By net% effect formula, we can calculate the total perecntage for 3 years tenure = 33.1% (sub details)

So, the difference between SI and CI = 36% – 33.1% = 2.9% (SI is more)

Here Aditya will get, 2.9% of 10000 = 290

So Aditya will have Rs. 290 more than Bhushan.

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Sub-details:-

 Net% effect = x + y = xy % 100

For the first 2 years: Here, x = y = 10%

 = 10 + 10 = 10 × 10 = 21% 100

And for the next year: Here x = 21% and y = 10%
 = 21 + 10 = 21 × 10 = 33.1% 100

Hence, option C is correct.

5
A sum of Rs. 9960 was borrowed at 15/2% per annum compound interest and paid back in two years in two equal annual installments. What was the amount of each installment?
» Explain it
B
Let the each instalment be x.

 x + x = 9960 ( 1 + 15 ) ( 1 + 15 ) 2 2 × 100 2 × 100

 x + x = 9960 ( 1 + 3 ) ( 1 + 3 ) 2 40 40

 ⇒ 40 x + 1600 x = 9960 43 1849

 ⇒ 1720 x + 1600 x = 9960 1849
⇒  3320 x = 9960 × 1849 ⇒  x = Rs. 5547

Hence, option B is correct.