The difference between
c.i. and s.i. accrued on an amount of rs. 20,000 in 2 years was rs. 392. find the rate of interest per annum. ticka 11.50% tickb 13% tickc 14% tickd 12%
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Simple interest accumulation factor :
Principle × rate × time
Principle = 20000
Time = 2
Calculations :
2 × 20000 × r = 40000r
The interest earned is :
40000r - 20000
The accumulation factor for compound interest:
P(1 + i)ⁿ
20000 × (1 + r)² = 20000(1 + i)²
Interest earned is :
20000(1 + r)² - 20000
Equating the two :
20000(1 + r)² - 20000 + 40000r - 20000 = 392
20000(1 + r)² - 40000 + 40000r = 392
20000(1 + r)² + 40000r = 392 + 40000
20000(1 + r)² + 40000r = 40392
Dividing through by 20000:
(1 + r)² + 2r = 2.0196
√(1 + r) ² + √2r = √2.0196
1 + r + 1.4142r^0.5 = 1.42113
r + 1.4141r^0.5 = 1.42113 - 1
r + 1.4141r^0.5 = 0.42113
Log r + 0.5 × 1.4141 log r = log 0.42113
log r + 0.70705 log r = - 0.37558
Log r (1 + 0.70705)
Log r = - 0.37558/1.70705 = - 0.22002
r = Log ⁻¹ (-0.22002) = 0.623 %
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