The compound interest on Rs 8000 at 20% per annum for 9 months compounded quarterly is:
a) 1260
b) 1261
c) 1271
d) 1281
Answer
Verified
Hint: Use the formula of compound interest $C.I.=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}-P$, where P is the principal (or original amount), r is the annual rate, n is the number of times interest compounded per time period, t is the number of years on which interest has applied.
Complete step-by-step answer:
We are going to use the formula of compound interest which is written below:
$C.I.=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}-P$
Where P: the Principal (or original amount)
r: annual rate of interest
n: number of times interest compounded per time period
t: number of years on which the interest has applied
It is given that:
The principal (or original amount) is Rs 8000.
Annual rate of interest is 20%.
The interest is compounding quarterly means n = 4.
The interest compounded quarterly for 9 months means $t=\dfrac{9}{12}$year.
Now, substituting these values in the compound interest formula we get,
$\begin{align}
& C.I.=8000{{\left( 1+\dfrac{20}{100\left( 4 \right)} \right)}^{4\times \dfrac{9}{12}}}-8000 \\
& C.I.=8000{{\left( 1+(0.25\times 0.2) \right)}^{3}}-8000 \\
& C.I.=8000{{\left( 1+.05 \right)}^{3}}-8000 \\
& C.I.=9261-8000 \\
& C.I.=1261 \\
\end{align}$
So, the compound interest on Rs 8000 at 20% per annum for 9 months compounded quarterly is 1261.
Hence, the correct option is (b).
Note:
While applying the formula of compound interest there are some common mistakes that could happen:
When substituting the value of r, don’t forget to divide the rate by 100.
There could be confusion with the “compounded quarterly” statement, it means in a year interest is 4 times compounded so n value will be 4.
And the “t” should be in years if in the question “t” is not given in years first convert it into years then apply in the formula.
The compound interest on Rs 16000 for 9 months at 20% per annum, interest being compounded quarterly, is = ?
A. Rs. 2520
B. Rs. 2524
C. Rs. 2522
D. Rs. 2518
Answer: Option C
Solution(By Examveda Team)
The interest is compounded quarterly,
$$\therefore R = \frac{{20}}{4} = 5\% $$
Time = 3 quarters
$$\eqalign{ &
\therefore C.I. = P\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^T} - 1} \right] \cr & = 16000\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^3} - 1} \right] \cr & = 16000\left[ {{{\left( {\frac{{21}}{{20}}} \right)}^3} - 1} \right] \cr & = 16000\left( {\frac{{9261 - 8000}}{{8000}}} \right) \cr & = 16000 \times \frac{{1261}}{{8000}} \cr & = {\text{Rs}}{\text{.}}\,\,2522 \cr} $$
Click here to read 1000+ Related Questions on Compound Interest(Arithmetic Ability)
- Aptitude
- Simple and compound interest
A) Rs. 2,520 |
B) Rs. 2,524 |
C) Rs. 2,522 |
D) Rs. 2,518 |
Correct Answer:
Description for Correct answer:
Principal= Rs. 16000,
Rate %=20 %
Time= 9 months
When interest is being compounded quaterly
Time=\( \Large \frac{9}{12} \times 4=3 \)
Rate =\( \Large \frac{20}{4} \%=5 \%=\frac{1}{20} \)
According to the question,
8000 units = Rs. 16000
1 unit = Rs. 2
1261 units = Rs.\( \Large 2 \times 1261\)
= Rs. 2522
Part of solved Simple and compound interest questions and answers : >> Aptitude >> Simple and compound interest
True
Explanation;
Hint:
Principal (P) = 16000
n = 9 months = `9/12` years
r = 20% p.a
For compounding quarterly, we have to use below formula,
Amount (A) = `"P" xx (1 + "r"/100)^(4"n")`
Since quarterly we have to divide ‘r’ by 4
r = `20/4` = 5%
A = `1600(1 + 5/100)^(9/12 xx 4)`
= `16000(105/100)^(9/12 xx 4)`
= `16000(105/100)^(9/3)`
= `16000 xx (21/20)^3`
= `16000 xx 21/20 xx 21/20 xx 21/20`
= 18522
∴ Interest A – P = 18522 – 16000 = 2522