The compound interest on a sum of money for years the on the same sum for the same period and at the same rate is 1280. Find the sum and the rate of interest per annum. sum and rate
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By formula amount C including compound interest after 2 years C = P(1+r/100)^2 - P
Amount S on the same sum P including the simple interest after 2 years S = P * 2 * r/100 = 2 P r/100
C /S =[ (1 + r/100)^2 - 1] / 2 r/100) = 1331.21 / 1280 = 1.04
100 [2 r/100 + r^2 /100^2] / (2 r) =
{2 r + r^2 / 100}/( 2 r) = 1.04
{200 + r} = 208
r = 208 - 200 = 8
Substitute in r = 8 in, S = 2 P r / 100 = 1280, we get: P = 1280*100/2 * 8 = 8000.
So the sum = 8000 rupees.
The rate of Interest = 8%
Amount S on the same sum P including the simple interest after 2 years S = P * 2 * r/100 = 2 P r/100
C /S =[ (1 + r/100)^2 - 1] / 2 r/100) = 1331.21 / 1280 = 1.04
100 [2 r/100 + r^2 /100^2] / (2 r) =
{2 r + r^2 / 100}/( 2 r) = 1.04
{200 + r} = 208
r = 208 - 200 = 8
Substitute in r = 8 in, S = 2 P r / 100 = 1280, we get: P = 1280*100/2 * 8 = 8000.
So the sum = 8000 rupees.
The rate of Interest = 8%
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