The difference between C.I. and S.I . on rs 20000 for 2 yrs is rs 128 at a same rate of interest per annum find the rate of interest
Answers
CI = P[1+r/100]^n-P
SI = pnr/100
From the problem,
P = 20,000
N = 2
CI – SI = 128
CI – SI = P[1+r/100]^n-P-Pnr/100
=P[(1+r/100)^n-1-nr/100]
Substituting the values of P and n, we get
CI – SI = 128 = 20000[(1+r/100)^2-1-2r/100]
Let us consider the expression within the square brackets, (1+r/100)^2-1-2r/100.
Expanding the square expression and subtracting the remaining terms, we get
1+2r/100+r^2/10000-1-2r/100 = r^2/10000
Thus, 128 = 20,000*r^2/10,000 = 2r^2
Or r^2 = 128/2 = 64.
Thus, r = 8%.
Therefore, the rate of interest is 8%.
Answer:
Rate = 8%
Step-by-step explanation:
For ,
N=2years
P=Rs20,000
We have S.I.=
PNR/100
=
20,000×2×R/100
=400R
And on interest being compounded for 2 years, Amount=P(1+ R/100) ²
=20,000×(1+ R/100) ²
=20,000×( 100+R/100) ²
=2R²+400R+20,000
So, C.I.=A−P=2R +400R+20,000−20,000=2R ² +400R
Given, C.I.−S.I=Rs128
=>2R ² +400R−400R=128
=>2R ² =128
=64
=>R=8 %