Question

two equal sums were lent at 5% and 6% per annunm compound interest for 2 years . if the difference in compound interest is rupees 422 . find _ i) the equal sums . ii) compound interset for each sum...

Answer 1

for 1st sum
p=p , r=5% , t=2years
a=p(1+r/100)n
a=p(1+5/100)2
a=(21/20)2 p
ci=a-p
ci=(21/20)2 p-p
ci=p{(21/20)2-1}

for 2nd sum
p=p , r=6% , t=2years
a=p(1+r/100)n
a=p(1+6/100)2
a=(53/50)2 p
ci=a-p
ci= {(53/50)2 p-p}
ci=p{(53/50)2 -1}
difference =ci of 2nd sum - ci of 1st sum
422=p{(53/50)2 -1} - p{(21/20)2 -1}
422=p{(53/50)2 -1 -(21/20)2 +1}
422=p{2809/2500 - 441/400}
422=p{211/10000}
p=422* 10000/211
p=20000

ci for 1st sum = p{(21/20)2 -1}
ci=20000(441/400 -1)
ci=20000*41/400
ci=2050

ci for 2nd sum = p{(53/50)2 -1}
ci =20000(2809/2500 -1)
ci =20000*309/2500
ci =2472

Answer 2

i) The equal sums are 20000 at 5%

                                   20000 at 6%

ii) Compound interest for each sum = RS 2050 interest in 5%

                                                              RS 2472 interest in 6%

To find:

i) The equal sums at 5% and 6%

ii) Compound interest for sums at 5% and 6%

Given data:

r = 5%, n = 2 years

r = 6%, n = 2 years

the difference in compound interest is rupees = RS 422

Formula:

$\mathrm{Cl}=\mathrm{P}\left(1+\frac{\mathrm{r}}{\mathrm{100}}\right)^{\mathrm{n}}$

$x+y+\frac{x y}{100}$

Solution:

r = 5%, n = 2 year

= $5+5+\frac{5 X 5}{100}$

= $5+5+\frac{25}{100}$

= 5 + 5 + 0.25

= 10.25%

r = 6%, n = 2 years

 = $6+6+\frac{6 X 6}{100}$

 = $6+6+\frac{36}{100}$

 = 6 + 6 + 0.36

 = 12.36%

the difference in compound interest is rupees = RS 422

that is 12.36% - 10.25% = RS 422

                            2.11% = RS 422

                    then 100% = ?

                                      = $\frac{422 X 100}{2.11}$

                                      = $\frac{42200}{2.11}$

                                      = RS 20000

P = 20000, N = 2, R = 5

$=\mathrm{20000}\left(1+\frac{\mathrm{5}}{\mathrm{100}}\right)^{\mathrm{2}}$ - 20000

$=\mathrm{20000}\left(\frac{\mathrm{105}}{\mathrm{100}}\right)^{\mathrm{2}}$ - 20000

= 20000 X $1.05^{2}$ - 20000

= 22050 - 20000

= RS 2050

P = 20000, N = 2, R = 6

  $=\mathrm{20000}\left(1+\frac{\mathrm{6}}{\mathrm{100}}\right)^{\mathrm{2}}$ - 20000

  $=\mathrm{20000}\left(\frac{\mathrm{106}}{\mathrm{100}}\right)^{\mathrm{2}}$ - 20000

  = 20000 X $1.06^{2}$ - 20000

  = 22472 - 20000

  = RS 2472

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