# Compound Interest Questions and Answers updated daily – Aptitude

## Compound Interest Questions

Investment in scheme A = Rs. x/2

According to the question,

A = P(1 + (R/100))

^{T}

x(1 + (20/100))

^{2}- x/2(1 + (10/100))

^{2}= 3507

x(6/5)

^{2}- x/2(11/10)

^{2}= 3507

36x/25 - 121x/200 = 3507

(288x - 121x)/200 = 3507

167x = 3507*200

x = (3507*200)/167

= Rs. 4200

^{T}- 1]

= P[(1 + 20/100)

^{2}- 1]

= P[(6/5)

^{2}- 1]

= P[(36/25) - 1] = Rs. 11P/25

SI = PTR / 100

= (11P/25) * (2*7.5/100)

= Rs. 33P/500

According to the question,

33P/500 + 11P/25 = 3036

(33P + 220P)/500 = 3036

253P = 3036*500

P = (3036*500)/253 = Rs. 6000

A = P(1 + R/100)

^{T}

13392 = 9300(1 + R/100)

^{2}

13392/9300 = (1 + R/100)

^{2}

144/100 = (1 + R/100)

^{2}

(12/10)

^{2}= (1 + R/100)

^{2}

12/10 = (1 + R/100)

R/100 = 12/10 - 1 = 2/10

R = (2/10)*100 = 20% p.a.

New rate = (R - 10)% = 10%

CI = P[(1 + R/100)

^{T}- 1]

= 9300[(1 + 10/100)

^{2}- 1]

= 9300[(11/10)

^{2}- 1]

= 9300(121/100 - 1)

= (9300*21)/100

CI = Rs. 1953

Time(T) = 4 Years

Rate of Interest (R) = 6% per year

To find Principal,

Formula to calculate Simple Interest:

SI = PRT/100

SI= Simple Interest; P=Principal

S.I. = (PRT)/100

1600 = (P*6*4)/100

1600*100 = P*24

(1600*100)/24 = P

P = Rs.6,667

Therefore, the sum of money is Rs.6,667.

To find compound interest (C.I.) for the same sum,

Formula for Compound Interest (C.I)

C.I. = [P*(1+R/100)

^{N}] â€“ P

C.I. = [6667*(1+6/100)

^{4}] â€“ 6667

C.I. = Rs. 1,750

Sum of money amounts in 2 yrs = Rs. 2420

Sum of money amounts in 3 yrs = Rs. 2662

So, interest on Rs.2420 for 1 yr = 2662 - 2420

= Rs. 242

**SI = PNR/100**

242 = (2420 x 1 x R)/100

R = (242 x 100)/2420

**R = 10%.**

Difference between CI and SI for 2 yrs = 20

**PR²/100² = 20**...(1)

Also given,

Difference between CI and SI for 3 yrs = 61

**PR²/100²[(300 + R)/100] = 61**

20[(300 + R)/100] = 61

300 + R = (61/20)*100

300 + R = 305

**R = 5%**

From (1),

P = 20*(100²/5²)

P = Rs. 8000

Therefore,

**sum is Rs.8000.**

Difference between CI and SI for 2 yrs = 832 - 800

**PR²/100²**= 832 - 800

PR²/100² = 32 .......(1)

SI for 2 yrs = Rs.800

**PNR/100**= 800

2PR/100 = 800 ....(2)

Divide (1) by (2),

R/200 = 32/800

**R = 8%**

Therefore,

**Principal = SI x(100/NR)**

Principal = (800 x 100)/(2 x 8)

**Principal = Rs. 5000**

Difference between CI and SI for 3 yrs =

**PR²(300 + R)/100³**

= (5000 x 8² x (300 + 8))/100³

=

**Rs. 98.56**

Rate of interest for 2 yrs = 20%

Rate of interest for last one yr = 125% of 20

= (125/100)*20 = 25%

WKT,

**A = P[1 + (r/100)]**

^{n}According to the question,

= 15,00,000{[1 + (20/100)]

^{2}[1 + (25/100)

^{1}]} - 15,00,000[1 + (20/100)]

^{3}

= 15,00,000{[1.2]

^{2}[1.25]} - 15,00,000[1.2]

^{3}

= 15,00,000(1.8 - 1.728)

= 15,00,000 x 0.072

= Rs.1,08,000

Required percentage = (108000/1500000)*100 =

**7.20%.**

**'Rs. x'.**

Therefore, Shyam share = Rs. (260200 - x)

WKT,

**A = P[1 + (R/100)]**

^{n}According to the question,amount recieved by Ram is same as that of Shyam,

x[1 + (4/100)]

^{4}= (260200 - x)[1 + (4/100)]

^{6}

x = (260200 - x)[1 + (4/100)]

^{2}

x = (260200 - x)[1 + (1/25)]

^{2}

x = (260200 - x)[26/25]

^{2}

x = (260200 - x) (676/625)

(625x/676) = 260200 - x

(625x/676) + x = 260200

(625x + 676x)/676 = 260200

1301x = 260200*676

x = (260200*676)/1301

x = Rs. 1,35,200

**Therefore, Ram's share is Rs. 1,35,200.**

Therefore, the amount invested in the scheme B = (40000 - X).

Given that the simple and compound interest for 1st year is same.

According to the question,

15% of X = 10% of (40000 - X)

15X/100 = (400000 - 10X)/100

15X = 400000 - 10X

15X + 10X = 400000

25X = 400000

X = Rs. 16,000

Amount invested in scheme B = 40000 - X

= 40000 - 16000

= Rs. 24,000

Therefore,

**Rs. 24,000**invested in scheme B.

râ‚ = 3%; râ‚‚ = 4%; râ‚ƒ = 5%

WKT, Amount = P[1 + (R/100)]

^{n}

A = P{(1 + (râ‚/100)) * (1 + (râ‚‚/100)) * (1 + (râ‚ƒ/100))}

= 2500{(1 + (3/100)) * (1 + (4/100)) * (1 + (5/100))}

= 2500(103/100) * (104/100) * (105/100)

A = Rs. 2811.90

CI = Amount - Principal

CI = 2811.90 - 2500

CI = Rs. 311.90

Time = n = 3/2 years = 3 half years

Formula for amount, A = P(1+(r/100))â¿

= 37500 (1+(4/100))Â³

= 37500 (1+(1/25))Â³

= 37500 (26/25)Â³

= Rs. 42812.4

Therefore, amount A = Rs. 42812.4

WKT, Amount = P[1 + (R/100)]

^{n}

Amount = [200(1 + (5/100))

^{3}] + [200(1 + (5/100))

^{2}] + [200(1 + (5/100)]

= [200(1 + (1/20))

^{3}] + [200(1 + (1/20))

^{2}] + [200(1 + (1/20)]

= [200(21/20)

^{3}] + [200(21/20)

^{2}] + [200(21/20)]

= [(200*9261)/8000] + [(200* 441)/400] + [210]

= 231.525 + 220.5 + 210

= Rs. 662.025

Therefore amount at the end of 3 years be Rs. 662.025.

WKT, Amount = P[1 + (R/100)]

^{n}

Sum of money amounts to Rs. 4840 in 2 yr,

4840 = P[1 + (r/100)]

^{2}....(i)

Sum of money amounts to Rs. 5324 in 3 yr,

5324 = P[1 + (r/100)]

^{3}.....(ii)

Dividing equation (ii) by (i), we get

5324/4840 = 1 + (r/100)

(5324/4840) - 1 = (r/100)

(5324 - 4840)/4840 = (r/100)

484/4840 = r/100

r = (484/4840)*100

r = 10%

Therefore, rate of interest per annum is 10%.

**Study the following information carefully and answer the given questions:**

A man invested Rs. 30000 in a scheme at 20% compound interest for 2 years. After 2 years he withdraws all his money. From that money, he purchased a Bike worth Rs. 32000. And with remaining amount, 10% in mutual funds and with the remaining money, he purchased 2 watches W1 and W2 for an equal amount. He sells watch W1 at 10% profit and watches W2 at 20% profit.

Refer the above for the Questions 55 to 54

Compound interest:

30000 * (20/100)= 6000

36000 * (20/100)= 72000

Compound Interest = 6000 + 7200

C.I = Rs.13200

The amount received after 2 years of his investment = 30000 + 13200 = Rs. 43200

It is given that, he purchased a Bike worth Rs.32000

Remaining amount = 43200 â€“ 32000 = Rs.11200

Total amount invested in Mutual funds = 11200*(10/100) = Rs. 1120

Remaining amount = 11200 â€“ 1120 = Rs. 10080

With this remaining amount, he purchased 2 watches W1 and W2 for an equal amount.

Cost price of W1 = Cost price of W2 = 10080/2 = Rs.5040

Selling price of W1 = 5040*(110/100) = Rs.5544

Selling price of W2 = 5040*(120/100) = Rs. 6048

**Study the following information carefully and answer the given questions:**

A man invested Rs. 30000 in a scheme at 20% compound interest for 2 years. After 2 years he withdraws all his money. From that money, he purchased a Bike worth Rs. 32000. And with remaining amount, 10% in mutual funds and with the remaining money, he purchased 2 watches W1 and W2 for an equal amount. He sells watch W1 at 10% profit and watches W2 at 20% profit.

Refer the above for the Questions 56 to 55

Compound interest:

30000 * (20/100)= 6000

36000 * (20/100)= 72000

Compound Interest = 6000 + 7200

C.I = Rs.13200

The amount received after 2 years of his investment = 30000 + 13200 = Rs. 43200

It is given that, he purchased a Bike worth Rs.32000

Remaining amount = 43200 â€“ 32000 = Rs.11200

Total amount invested in Mutual funds = 11200*(10/100) = Rs. 1120

Remaining amount = 11200 â€“ 1120 = Rs. 10080

With this remaining amount, he purchased 2 watches W1 and W2 for an equal amount.

Cost price of W1 = Cost price of W2 = 10080/2 = Rs.5040

Selling price of W1 = 5040*(110/100) = Rs.5544

**Study the following information carefully and answer the given questions:**

A man invested Rs. 30000 in a scheme at 20% compound interest for 2 years. After 2 years he withdraws all his money. From that money, he purchased a Bike worth Rs. 32000. And with remaining amount, 10% in mutual funds and with the remaining money, he purchased 2 watches W1 and W2 for an equal amount. He sells watch W1 at 10% profit and watches W2 at 20% profit.

Refer the above for the Questions 57 to 56

Compound interest:

30000 * (20/100)= 6000

36000 * (20/100)= 72000

Compound Interest = 6000 + 7200

C.I = Rs.13200

The amount received after 2 years of his investment = 30000 + 13200 = Rs. 43200

It is given that, he purchased a Bike worth Rs.32000

Remaining amount = 43200 â€“ 32000 = Rs.11200

Total amount invested in Mutual funds = 11200*(10/100) = Rs. 1120

Remaining amount = 11200 â€“ 1120 = Rs. 10080

**Study the following information carefully and answer the given questions:**

A man invested Rs. 30000 in a scheme at 20% compound interest for 2 years. After 2 years he withdraws all his money. From that money, he purchased a Bike worth Rs. 32000. And with remaining amount, 10% in mutual funds and with the remaining money, he purchased 2 watches W1 and W2 for an equal amount. He sells watch W1 at 10% profit and watches W2 at 20% profit.

Refer the above for the Questions 58 to 57

Compound interest:

30000 * (20/100)= 6000

36000 * (20/100)= 72000

Compound Interest = 6000 + 7200

C.I = Rs.13200

The amount received after 2 years of his investment = 30000 + 13200 = Rs. 43200

It is given that, he purchased a Bike worth Rs.32000

Remaining amount = 43200 â€“ 32000 = Rs.11200

**Study the following information carefully and answer the given questions:**

A man invested Rs. 30000 in a scheme at 20% compound interest for 2 years. After 2 years he withdraws all his money. From that money, he purchased a Bike worth Rs. 32000. And with remaining amount, 10% in mutual funds and with the remaining money, he purchased 2 watches W1 and W2 for an equal amount. He sells watch W1 at 10% profit and watches W2 at 20% profit.

Refer the above for the Questions 59 to 58

Compound interest:

30000 * (20/100)= 6000

36000 * (20/100)= 72000

Compound Interest = 6000 + 7200

C.I = Rs.13200

The amount received after 2 years of his investment = 30000 + 13200 = Rs. 43200

Reet invested an amount = Rs.A

Sonali invested an amount = Rs. (A + 1500)

According to the question, same amount of interest is received by both.

Therefore, CI = SI

P[1 + (R/100)]â¿ - P = PNR/100

A(1 + (12/100))² - A = [(A + 1500)*3*8%]

A*(112/100)*(112/100) - A = (A + 1500)*(24/100)

A*(12544/10000) - A = A*(24/100) + (1500*(24/100))

A*(12544/10000) - A - A*(24/100) = 360

(12544A - 10000A - 2400A)/10000 = 360

144A = 3600000

A = Rs. 25,000

Amount invested by Reet = Rs. 25,000.