Calculate the amount and the compound interest on Rs. 6000 for 2 years when the rates of interest for successive years are 5% and 6% respectively.
plz give the correct answer with all steps.
Answers
✨ Answer ✨
At first, find the amount after the first year by the given principal interest rate for first year and time, which is, one year using formula,
A=P(1+r100)n
Where, A is the amount, P is principal, r is rate and n is number of years. Then, use the amount as principal for the second year and thus, find the amount for second year. Then, to find compound interest, subtract the original principal from the amount obtained after two years.
Complete step-by-step answer:
So, we will find the amount year wise at first, we will find the amount after 1 year and then, after the second year.
So, for the first year, we will find out the amount after the first year by using the formula to find amount which is,
A=P(1+r100)n
Where, A is the amount, P is principal, r is rate and n is number of years.
So, here the principal value is Rs.6000, rate is 5% and number of years is 1. Hence, the amount will be,
A=6000(1+5100)1
We can further simplify it as,
A=6000×105100⇒A=60×105=6300
So, the amount will be Rs.6300 which will be the principal value for second year.
So, for the second year, the principal amount will be Rs.6300, rate of interest will be 6% and time will be 1 year. Hence, the amount obtained will be,
A=P(1+r100)n
On substituting, we get,
A=6300(1+6100)1
Now, on simplifying we get,
A=6300×106100⇒A=63×106=6678
So, the amount obtained after the two years is Rs.6678. The original principal value was Rs.6000. So, we can find the compound interest by subtracting principal value from the amount.
Hence, compound interest is {Rs.6678−Rs.6000}⇒Rs.678
Hence, the amount is Rs.6678 and the compound interest is Rs.678.
Note: Instead of finding amount year wise, one can also find it with using one formula, which is, A=P(1+r1100)(1+r2100)
, where, r1 and r2
are given rates of interest. Using this formula saves a lot of time by avoiding the calculations and also chances of committing a silly mistake are less. So, if you remember this formula, go for this during exams
Give me some multiple thanks please
STEP BY STEP EXPLANATION:-
So, we will find the amount year wise at first, we will find the amount after 1 year and then, after the second year.
So, for the first year, we will find out the amount after the first year by using the formula to find amount which is,
A = P( 1 + r/100 )^ n
Where, A is the amount, P is principal, r is rate and n is number of years.
So, here the principal value is Rs.6000, rate is 5% and number of years is 1. Hence, the amount will be,
A = 6000( 1 + 5/100 )^ 1
We can further simplify it as
A = 6000 × 105/100
⇒A = 60 × 105 = 6300
So, the amount will be Rs.6300 which will be the principal value for second year.
So, for the second year, the principal amount will be Rs.6300, rate of interest will be 6% and time will be 1 year. Hence, the amount obtained will be,
A = P( 1 + r/100 )^ n
Now, on simplifying we get,
A = 6300( 1 + 6/100 )^ 1
⇒ A = 63 × 106 = 6678
So, the amount obtained after the two years is Rs.6678. The original principal value was Rs.6000. So, we can find the compound interest by subtracting principal value from the amount.
Hence, compound interest is
{ Rs.6678 − Rs.6000 }⇒ Rs.678
Hence, the amount is Rs.6678 and the compound interest is Rs.678.
NOTE :
Instead of finding amount year wise, one can also find it with using one formula,
which is, A=P( 1 + r1/100 ) ( 1 + r2/100 )
where, r1 and r2
are given rates of interest. Using this formula saves a lot of time by avoiding the calculations and also chances of committing a silly mistake are less. So, if you remember this formula, go for this during exams.