In what time will ₹ 1500 yield ₹ 496.50 as compound interest

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(i) In what time will ₹ 1500 yield ₹ 496.50 as compound interest at 10% per annum compounded annually?
(ii) Find the time (in years) in which ₹ 12500 will produce ₹ 3246.40 as compound interest at 8% per annum, interest compounded annually.

Solution:

(i) It is given that
Principal (P) = ₹ 1500
CI = ₹ 496.50
So the amount (A) = P + SI
Substituting the values
= 1500 + 496.50
= ₹ 1996.50
Rate (r) = 10% p.a.
We know that
A = P (1 + r/100)n
It can be written as
A/P = (1 + r/100)n
Substituting the values
1996.50/1500 = (1 + 10/100)n
By further calculation
199650/(1500 × 100) = (11 /10)n
So we get
1331/1000 = (11/10)n
(11/10)3 = (11/10)n
Here Time n = 3 years
(ii) It is given that
Principal (P) = ₹ 12500
CI = ₹ 3246.40
So the amount (A) = P + CI
Substituting the values
= 12500 + 3246.40
= ₹ 15746.40
Rate (r) = 8% p.a.
We know that
A = P (1 + r/100)n
It can be written as
A/P = (1 + r/100)n
Substituting the values
15746.40/12500 = (1 + 8/100)n
Multiply and divide by 100
1574640/ (12500 × 100) = (27/25)n
By further calculation
78732/ (12500 × 5) = (27/ 25)n
19683/ (3125 × 5) = (27/25)n
So we get
19683/15625 = (27/25)n
(27/25)3 = (27/25)n
Here Period = 3 years

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