The difference between the compound interest and the simple interest on 42000 for two years is 105 at the same rate of interest per annum. Find (i) the rate of interest and (ii) the compound interest earned in second year.
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The difference between the compound interest and the simple interest on 42000 for two years is 105 at the same rate of interest per annum. Find (i) the rate of interest and (ii) the compound interest earned in second year.
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Step-by-step explanation
We have the difference
We have the differenceS.I - C.I = 105
We have the differenceS.I - C.I = 105And the principle value = 42000
We have the differenceS.I - C.I = 105And the principle value = 42000We know the formula of simple interest
We have the differenceS.I - C.I = 105And the principle value = 42000We know the formula of simple interest=P.R.T100
Here P = principle value, R = rate of interest and T= time
Putting the values in the formula
Putting the values in the formula=42000.r.2100
Putting the values in the formula=42000.r.2100=840r
Now we have to find the compound interest
Now we have to find the compound interestA = P(1+r100)t
Now we have to find the compound interestA = P(1+r100)tHere A = final amount
Now we have to find the compound interestA = P(1+r100)tHere A = final amountPutting the values
=42000(1+r100)2
= 42000(1+r10000+r50)
=42000+42r210+840r
Now we know that
C.I = A – P
C.I = 42000+42r210+840r
−42000
C.I = =42r210+840r
We have given in the question that the difference between the S.I and C.I is 105
S.I – C.I = 105
840r+
42r210−840r=105
42r210=105
42r2=105.10
r2=105.1042
r2=25
r=25−−√
r=5
Interest rate is 5
So, we have a rate of interest of 5%.
So, we have a rate of interest of 5%.Now we have to find the compound interest at second year
So, we have a rate of interest of 5%.Now we have to find the compound interest at second year We can find the compound interest
C.I = A – P
C.I = 42000(1+5100)2−42000
C.I = 42000(1+2510000+110)−42000
Therefore Rs = 4305
Note: Simple interest is based on the principal amount of a loan. Compound interest is based on the principal amount and the interest which is being added for every period of time.
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