A sum of money invested at compound interest amounts to rs. 4624 after 2 years and to rs.4924 after 3 years the sum of money is
Answers
Answer:
The sum of money invested ≅ Rs 66929
Step-by-step explanation:
The sum of money invested is the initial Principle Amount = P
1st Year:
Compound Interest C.I = PTR / 100
Let C.I for the 1st year = x
x = (P x 1 x R) / 100
R = (x x 100) / P ……. Eq (1)
Amount at the end of 1st year A = P + x ……. Eq (2)
2nd Year:
Compound Interest C.I = P1TR / 100
P = A
Given C.I for the 2nd year = Rs 4624
4624 = (A x 1 x R) / 100
R = (4624 x 100) / A …… Eq(3)
Amount at the end of 2nd year A1 = A + 4624 …… Eq(4)
3rd Year:
Compound Interest C.I = PTR / 100
P = A1
Given C.I for the 3rd year = Rs 4924
4924 = (A1 x 1 x R) / 100
R = (4924 x 100) / A1 …… Eq(5)
Solving Eq(3) & Eq(5):
R = (4624 x 100) / A
R = (4924 x 100) / A1
From Eq(4),
A1 = A + 4624
(4624 x 100) / A = (4924 x 100) / A1
(4624 x 100) / A = (4924 x 100) / (A + 4624)
4624 / A = (4924) / (A + 4624)
(A + 4624)(4624) = (4924)A
A + 4624 = 1.06487889A
1.06487889A - A = 4624
A(1.06487889 - 1) = 4624
0.06487889A = 4624
A = 71271.2563 …… Eq(6)
Solving Eq(1) & Eq(3):
R = (x x 100) / P
R = (4624 x 100) / A
From Eq(2),
A = P + x
P = A - x
(x x 100) / P = (4624 x 100) / A
(x x 100) / (A - x) = (4624 x 100) / A
x / (A - x) = 4624 / A
Ax = 4624 (A - x)
Ax = 4624A - 4624x
(A + 4624)x = 4624A
From Eq(6),
A = 71271.2563
(71271.2563 + 4624)x = (4624)(71271.2563)
75895.2563x = 329558289
x = 4342.27783
From Eq (2),
A = P + x
P = A - x
= 71271.2563 - 4342.27783
= 66928.9785
≅ 66929
Therefore, the sum of money invested P ≅ Rs 66929