Answer
Hint: Use compound interest formula for the calculation of amount $A$, given by:
\[A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}\]. From this, calculate amount $A$ after $t=1$ year.
Then subtract the principal amount $P$ from the amount $A$ to get the interest.
Complete step-by-step answer:
Compound interest is the addition of interest to the principal sum of a loan or deposit. It is the result of reinvesting interest, rather than paying it out, so the interest in the next
period is then earned on the principal sum plus previously accumulated interest.
The total accumulated amount $A$ , on the principal sum \[P\] plus compound interest $I$ is given by the formula \[A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}\].
Here, \[A\] is the amount obtained, $t$ is the number of years, \[r\] is the rate, $P$ is the principal and \[n\] is the number of times the interest is given in a year.
The total compound interest generated is given by: $I=A-P$.
Now, we have been given that:
$P=\text{Rs}\text{. }10000\text{ , }r=8%=\dfrac{8}{100}\text{ , }t=1\text{ year and }n=2$
Therefore, amount credited in 1 year,
$\begin{align}
& A=10000\times {{\left( 1+\dfrac{8}{2\times 100} \right)}^{2\times 1}} \\
& =10000\times {{\left( 1+\dfrac{4}{100} \right)}^{2}} \\
& =10000\times {{\left( \dfrac{104}{100} \right)}^{2}} \\
& ={{\left( 104 \right)}^{2}} \\
&
=10816 \\
\end{align}$
Also, compound interest will be
$\begin{align}
& I=A-P \\
& =10816-10000 \\
& =816 \\
\end{align}$
Hence, the amount and interest in 1 year will be Rs. 10816 and Rs. 816 respectively.
Therefore, option (a) is the correct answer.
Note: We have used the value of $n$ equal to 2 because $n$ represents the number of times the interest is compounded in a year. In the question it was given that interest is compounded half-yearly, that means one time in half a year. Therefore, in one year it will be two times. Hence, $n=2$ is used.
Calculate the amount and compound interest on (a) ₹ 10,800 for 3 years at 12(1/2)% per annum compounded annually (b) ₹ 18,000 for 2(1/2) years at 10% per annum compounded annually (c) ₹ 62,500 for 1(1/2)years at 8% per annum compounded half yearly (d) ₹ 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify) (e) ₹ 10,000 for 1 year at 8% per annum compounded half yearly
Solution:
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- Calculate the amount and compound interest on (a) ₹ 10,800 for 3 years at 12(1/2)% per annum compounded annually (b) ₹ 18,000 for 2(1/2) years at 10% per annum compounded annually (c) ₹ 62,500 for 1(1/2)years at 8% per annum compounded half yearly (d) ₹ 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify) (e) ₹ 10,000 for 1 year at 8% per annum compounded half yearly
- Calculate the amount and compound interest on(a) ₹ 10,800 for 3 years at 12(1/2)% per annum compounded annually(b) ₹ 18,000 for 2(1/2) years at 10% per annum compounded annually(c) ₹ 62,500 for 1(1/2)years at 8% per annum compounded half yearly(d) ₹ 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify)(e) ₹ 10,000 for 1 year at 8% per annum compounded half yearly
- What will be the compound interest on rupees 10000 for 1 year at 8% per annum if the interest is compounded half yearly?
- What is the amount on ₹ 10000 for 1 year at 8 per annum compounded half yearly?
- What is compound interest on an amount of Rs 10000 at 8% per annum for 2 years?
- What would be the compound interest on an amount of Rs 10000 at the rate of 5% for one year?
What is known: Principal, Time Period and Rate of Interest
What is unknown: Amount and Compound Interest (C.I)
Reasoning:
A = P[1+(r/100)]n
Steps:
(i)
P = ₹ 10800
N = 3 years
R = 12(1/2)% = (25/2)% compounded annually
A = P[1+(r/100)]n
A = 10800[1+(25/(2×100))]3
A = 10800 (225/200)3
A = 10800 × (225/200) × (225/200) × (225/200)
A = 15377.34
C.I. = A - P
= 15377.34 - 10800
= 4577.34
Answer: Amount = ₹ 15377.34
Compound Interest = ₹ 4577.34
(ii)
P = ₹ 18000
N = 2(1/2) years
R = 10% compounded annually
A = P[1+(r/100)]n
Since 'n' is 2(1/2) years, amount can be calculated for 2 years and having amount as principal Simple Interest(S.I.) can be calculated for 1/2 years because C.I. is only annually
A = P[1+(r/100)]n
A = 18000[1+(10/100)]2
A = 18000 × (11/10) × (11/10)
A = 21780
Amount after 2 years = ₹ 21870
S.I. for 1/2 years = 1/2 × 21780 × 10/100
= 1089
Amount after 2(1/2) years = 21780+1089
= ₹ 22869
C.I. after 2(1/2) years = 22869 - 18000
= ₹ 4869
Answer: Amount = ₹ 22869
Compound Interest = ₹ 4869
(iii)
P = ₹ 62,500
N = 1(1/2) years
R = 8% compounded half yearly
A = P[1+(r/100)]n
There are 3 half years in 1(1/2) years. Therefore, compounding has to be done 3 times and rate of interest will be 4%.
A = P[1+(r/100)]n
A = 62500[1+(4/(100)]3
A = 62500 (104/100)3
A = 62500 × (104/100) × (104/100) × (104/100)
A = 70304
C.I. = A - P
= 70304 - 62500
= 7804
Answer: Amount = ₹ 70304
Compound Interest = ₹ 7804
(iv)
P = ₹ 8000
n = 1 year
R = 9% p.a. compounded half yearly
A = P[1+(r/100)]n
S.I. for 1st 6 months = (1/2) × 8000 × (9/100)
= 40 × 9
= 360
Amount after 1st 6 months including Simple Interest = 8000 + 360
= ₹ 8360
Principal for 2nd 6 months = ₹ 8360
S.I. for 2nd 6 months = 1/2 × 8360 × 9/100
= (418×9)/100
= 376.20
C.I. after 1 year (9% p.a. interest half yearly) = 360 + 376.20
= 736.20
Amount after 1 year (9% p.a. interest half yearly) = 8000 + 736.20
= 8736.20
Answer: Amount = ₹ 8736.20
Compound Interest = ₹ 736.20
(v)
P = ₹ 10,000
n = 1 year
R = 8% p.a. compounded half yearly
A = P[1+(r/100)]n
There are 2 half years in 1 years. Therefore, compounding has to be done 2 times and rate of interest will be 4%
A = P[1+(r/100)]n
A = 10000[1+(4/100)]2
A = 10000 × (104/100) × (104/100)
A = 10816
C.I. after 1 year (8% p.a. interest half yearly) = 10816 - 10000
= 816
Amount after 1 year (8% p.a. interest half yearly) 10816 = 10816
Answer: Amount after 1 year = ₹ 10816
Compound Interest after 1 year = ₹ 816
☛ Check: NCERT Solutions for Class 8 Maths Chapter 8
Video Solution:
Calculate the amount and compound interest on(a) ₹ 10,800 for 3 years at 12(1/2)% per annum compounded annually(b) ₹ 18,000 for 2(1/2) years at 10% per annum compounded annually(c) ₹ 62,500 for 1(1/2)years at 8% per annum compounded half yearly(d) ₹ 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify)(e) ₹ 10,000 for 1 year at 8% per annum compounded half yearly
NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.3 Question 1
The amount and compount interest are (i) ₹ 15377.34 and ₹ 4577.34 (ii) ₹ 22869 and ₹ 4869 (iii) ₹ 70304 and ₹ 7804 (iv) ₹ 8736.20 and ₹ 736.20 (v) ₹ 10816 and ₹ 816
☛ Related Questions:
- Vasudevan invested ₹ 60,000 at an interest rate of 12% per annum compounded half-yearly. What amount would he get (i) after 6 months? (ii) after 1 year?
- Arif took a loan of ₹ 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1(1/2) years if the interest is (i) Compounded annually (ii) Compounded half-yearly
- Maria invested ₹ 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find: (i) The amount credited against her name at the end of the second year (ii) The interest for the 3rd year.
- Find the amount and the compound interest on ₹ 10,000 for 1(1/2) years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
What will be the compound interest on rupees 10000 for 1 year at 8% per annum if the interest is compounded half yearly?
(10816 - 10000) = Rs. 816.
What is the amount on ₹ 10000 for 1 year at 8 per annum compounded half yearly?
<br> Rs 10,000 for 1 year at 8% per annum compounded half yearly. Calculate the amount and compound interest on : Rs 62,500 for `1(1)/(2)` years at 8% per annum compounded half yearly.
What is compound interest on an amount of Rs 10000 at 8% per annum for 2 years?
Solution. ∴ Compound interest is ₹ 1698.58.
What would be the compound interest on an amount of Rs 10000 at the rate of 5% for one year?
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