Compound Interest

Given, total amount (to be shared by two sons at the age of 20 on Compound interest) = ₹ 16,400
Let the Present share (Principal amount) for 17 year old son = "X"
Then the Present share (Principal amount) for 18 year old son = (16,400 - X)
To attain 20 years of age,
⇒ 17 year old son takes 3 years (N = 3 years on Compound interest)
⇒ 18 year old son takes 2 years (N = 2 years on Compound interest)
Given, Rate of interest (R) = 5%
at the age of 20, two sons get equal amount
⇒ Compound Amount of 17 year old son = Compound Amount of 18 year old son
W.K.T, Formula for Compound Amount = P [1 + (R/100)]^N
⇒ X (1 + 5/100)^3 = (16,400 - X) (1 + 5/100)^2
⇒ X (1 + 5/100) = (16,400 - X)
⇒ (105/100) X = (16,400 - X)
⇒ [(105/100) X] + X = 16,400
⇒ 205 X = 16,400 × 100
⇒ X = 16,40,000 / 205
⇒ X = 8,000
∴ Present share for 17 year old son = ₹ 8,000

Principal : P = 10000 ₹ Rate of Interest : r = 4 % Number of years : n = 2 Amount = P×(1 + r/100)^n Amount = 10000×(1+4/100)^2 =10000×(1+$$\frac{1}{2}$$5)^2 =10000×(26/25)×(26/25) =10816

Suppose the person has deposited ₹ X at the time of opening account.
⇒ After one year, he had
⇒ ₹ (x +x × 10 × 1/100) = ₹ (11x/10)
⇒ After two years, he had
⇒ ₹((11x/10)+(11x/10) × (10 × 1/100)) = (121x/100)
⇒ After withdrawing ₹ 5000 from ₹ (121x/100) ,the balance
⇒ = ₹ (121x - 500000/100)
⇒ After 3 years, he had
⇒ ((121x - 500000/100) + (121x - 500000/100) × (10 × 1/100))
⇒ = 11(121x - 500000/1000)
⇒ After withdrawing 6000 from above, the balance
⇒ = ₹(1331x/1000) - 11500
⇒ After 4 years, he had
⇒ ₹(11/10) ((1331x/1000) - 11500) - 10000 = 0
⇒ ₹ 15470
Hence, option (A) is correct.

We know, Amounts that lend on S.I. and C.I. after 2 yearss is in the ratio of 520 : 529.
Let the amount received after 2 yearss be 520X and 529X.
Given that difference between interest earned in two years is ₹18.
529X - 520X = 18
9X = 18
X = 2
Amount received after 2 yearss on SI = 520X = 520(2) = ₹ 1040
Amount received after 2 yearss on CI = 529X = 529(2) = ₹ 1058
Amount invested in both scheme for 3yrs = ₹ 1600
Given that amount invested and rates on each scheme is equal.
Principal invested in each scheme = 1600/2 = ₹ 800
SI = PNR/100;
R = (SI×100)/PN
Where, SI = 1040 - 800 = ₹ 240
R = (240×100)/(800×2)
R = 15%
SI after 3 yearss = (800×3×15)/100 = ₹ 360
CI after 3 yearss = P [(1 + r/100)ⁿ - 1]
= 800[(1 + 15/100)³ - 1]
= 800[(23/20)³ - 1]
= 800[(12167 - 8000)/8000]
= ₹ 416.7
Required ratio = 360/416.7 = 400/463.

We know, CI: P = ₹ 12,000; N = 2 yearss; R = 5%
C.I. = P[(1+R/100)^N] – P
CI for 1st yr = 12000[1 + (5/100)] - 12000
= 12000[(2$$\frac{1}{2}$$0) - 1]
= 12000[(21- 20)/20]
= ₹ 600
Principal for 2nd yr = 12000 + 600 = ₹ 12, 600
CI for 2nd yr = 12600[1 + (5/100)] - 12600
= 12600[(2$$\frac{1}{2}$$0) - 1]
= 12600[(21- 20)/20]
= ₹ 630
CI for 2 yearss = 600 + 630 = ₹ 1,230
Given: SI is 5/6 of CI,
SI = (5/6)×1230
SI = ₹ 1025
SI = PNR/100
1025 = [P×5×10]/100
P = [1025×100]/[5×10]
P = ₹ 2050.

Solution is :
Given principal = 6500
No. of years = 2
Rate of interest = 15
Amount = P [ 1 + ( r / 100 )ⁿ]
= 6500×[ 1 + ( 15 /100 )²]
= 6500×[ 1 + ( 3 / 20 )²]
= 6500×[ 23 / 20 ]²
= 6500×[ 529 / 400 ]
Amount =8596.25
Compound Interest = Amount - Principal
= 8596.25 - 6500
= 2096.25

We know, Madhu invested ₹ X ; N = 2 yearss; R = 15% and CI = ₹ 5,805
CI = P[1 + (R/100)]^N - P
5805 = X[1 + (15/100)]² - X
5805 = X[23/20]² - X
5805 = X[(529 - 400)/400]
X = 5805×(400/129)
X = ₹ 18,000
If Madhu invested ₹ (X + 14000); N = 2 yearss; R = 30%(additional rate of 15%)
CI = (18000 + 14000)[1 + (30/100)]² - (18000 + 14000)
CI = 32000[13/10]² - 32000
CI = 32000[(169 - 100)/100]
CI = 32000[69/100]
CI = ₹ 22,080.

Amount = ₹ (9300 + 4092) = ₹ 13392
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 = ₹ 1953

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