Free Practice Questions for Simple-and-compound-interest in Maths
Practice questions here, for every subject and every exam. Unlimited questions for unlimited attempts, given with answers and explanations.
Question 61:
Sumit invested Rs. 50,000 each in two banks for 2 years. The first bank gives simple interest at the rate of $11 \%$ per annum, while the other bank gives compound interest, compounded annually at the rate of $10 \%$ per annum. How much interest did he earn from the two banks in 2 years?
Correct Answer: 4
Given:
Amount $=$ Rs. 50000 each, Time $=2$ years and Interest rate in first bank $=11 \%$ p.a. SI and in second bank $=10 \%$ p.a. $\mathrm{Cl}$
Interest from first bank $=$ Amount $\times$ Rate $\times$ Time
$
=50000 \times 11 \% \times 2=\text { Rs. } 11000
$
Interest form second bank $=\left[\right.$ Amount $\left.\times(1+R)^{\top}\right]-$ Amount
$
\begin{aligned}
&=\left[50000 \times(1+10 \%)^{2}\right]-50000 \\
&=\left[50000 \times(1.1)^{2}\right]-50000 \\
&=(50000 \times 1.21)-50000 \\
&=60500-50000=\text { Rs. } 10500
\end{aligned}
$
Total interest from both the banks $=11000+10500=$ Rs. 21500
Question 62:
A sum increases by $75 \%$ in 10 years at certain rate of simple interest per annum. By what percentage will the same sum increase in 6 years at the same rate of simple interest per annum?
Correct Answer: 2
Clearly, Rate $=\frac{75}{10}=7.5 \%$, Time $=6$ year
So, Required percentage $=7.5 \times 6$ $=45 \%$
Question 63:
The difference between the interest payable on a sum invested for three years at 20 % compound interest per annum compounded annually and 20% simple interest per annum for the same period is ₹ 448 . What is the value of the sum invested?
Correct Answer: 1
Rate $=20 \%$
$=\frac{1}{5}$
Time $=3$ years
Let the sum invested be $(5)^{3}=125$
Then, $\mathrm{SI}=\frac{125 \times 20 \times 3}{100}=75$
Now, For CI,
$\mathrm{CI}=25 \times 3+5 \times 3+1=91$
$\begin{aligned} \mathrm{CI}-\mathrm{SI} &=91-75 \\ &=16 \end{aligned}$
ATQ,
$16 \rightarrow 448$
So, Sum $\Rightarrow 125=\frac{448}{16} \times 125$
$=28 \times 125$
$=3500$ Rupees
Question 64:
A certain sum on compound interest becomes ₹ 56,180 when compounded annually after 2 years and ₹ 59,550.80 after 3 years.
Find the sum (in ₹).
Correct Answer: 4
Clearly,
Rate $=\frac{59550.8-56180}{56180} \times 100$
$=\frac{3370.8}{56180} \times 100$
$=6 \%$
No, Let the Principal be $P$, then
According to Question,
$56180=\mathrm{P}\left(1+\frac{6}{100}\right)^{2}$
$\Rightarrow P=\frac{56180 \times 50 \times 50}{53 \times 53}$
$=20 \times 50 \times 50$
$=50,000$ Rupees
Question 65:
Out of a total sum of ₹ 5,000, Danish invested one part at 12 % simple interest per annum and the remaining part at 10 % simple interest per annum. If the total interest that accrued to Danish in two years equals ₹ 1072, what was the sum Danish invested at 12 % simple interest per annum?
Correct Answer: 1
Net Interest Rate $=\frac{1072}{5000 \times 2} \times 100$
$=10.72 \%$
Now,
$
\Rightarrow \mathrm{I}: \mathrm{II}=9: 16
$
So, Sum Invested at $12 \%$,
$
I=\frac{5000}{9+16} \times 9=1800 \text { rupees }
$
Question 66:
A person invested one-third of his money at $3 \frac{1}{2} \%$, one-fourth of his money at $7 \frac{1}{2} \%$, and the remaining at $8 \%$ per annum simple interest. If his yearly simple interest is $₹ 1,479$, then what is the sum invested (in ₹)?
Correct Answer: 2
Question 67:
What will be the amount after 2 years, if a sum of ₹ 2,200 is invested at $12 \%$ per annum compound interest, compounded half-yearly (correct to two decimal places)?
Correct Answer: 3
Question 68:
The simple interest on a certain sum for $3 \frac{1}{3}$ years at $15 \%$ p.a. is ₹ 1,840 less than the simple interest on the same sum for $5 \frac{1}{2}$ years at $12 \%$ p.a. The sum is:
Correct Answer: 4
Clearly, $\left(\frac{11}{2} \times 12-\frac{10}{3} \times 15\right) \%$ of sum $=1840$
$\Rightarrow(66-50) \%$ of sum $=1840$
$
\begin{aligned}
&\Rightarrow \text { sum }=\frac{1840}{16} \times 100 \\
&=11500 \text { Rupees }
\end{aligned}
$
Question 69:
The amount payable on maturity after $5 \frac{1}{2}$ years on a sum of ₹ 4,750 , when invested at a certain rate per cent of simple interest per annum, was ₹$ 6,840$. What was the per annum per cent rate of simple interest paid?
Correct Answer: 2
Clearly,$(6840-4750)=\frac{4750 \times R \times 11}{100 \times 2}$
$\Rightarrow 2090=\frac{4750 \times 11 R}{200}$
$\Rightarrow R=\frac{2090 \times 200}{4750 \times 11}$
$=8 \%$
Question 70:
A certain sum is invested on compound interest at $18 \%$ per annum for 1 year 4 months, the interest being compounded 8-monthly. If the compound interest is ₹ 3,816, then find the sum (in ₹).
Correct Answer: 4
Time $=1$ years 4 months $=16$ months
$=2$ cycles of 8 months
Rate $=18 \%$ per annum
$=\frac{18}{12} \times 8 \%$ per 8 months
$=12 \% / 8$ months
Now $R=12 \%, T=2$
Let the sum be $P$
then, $3816=P\left(1+\frac{12}{100}\right)^{2}-P$
$\Rightarrow 3816=P \times \frac{28 \times 28}{25 \times 25}-P$
$\Rightarrow 3816=\frac{P\left(28^{2}-25^{2}\right)}{625}$
$\Rightarrow 3816 \times 625=159 \mathrm{P}$
$\Rightarrow \mathrm{P}=\frac{3816 \times 625}{159}$
$\Rightarrow \mathrm{P}=15000$ rupees.
Question 71:
A sum of ₹7800 amounts to ₹ $10381.80$ at $x \%$ p.a. in 2 years when the interest is compounded 8-monthly. What will be the compound interest on the same sum at $(x+5) \%$ p.a. in one year, if the interest is compounded half yearly?
Correct Answer: 4
Time 2 years $=24$ months $=3$ cycles of 8 months $\mathrm{R}=x \%$ P.a. $=\frac{x}{12} \times 8 \%$ per 8 months
$=\frac{2 x}{3} \%=r \% \text { (say) }$
Now, $10381.8=7800\left(1+\frac{r}{100}\right)^{3}$
$
\Rightarrow\left(1+\frac{r}{100}\right)^{3}=\frac{10381.8}{7800}=\frac{103818}{78000}
$
$
\Rightarrow\left(1+\frac{r}{100}\right)^{3}=\frac{1331}{1000}
$
$
\Rightarrow\left(1+\frac{r}{100}\right)^{3}=\left(\frac{11}{10}\right)^{3}
$
$\Rightarrow 1+\frac{r}{100}=\frac{11}{10}$
$\Rightarrow \mathrm{r}=10 \% \Rightarrow \frac{2 x}{3}=10 \% \Rightarrow x=15 \%$
Now $\mathrm{R}=(x+5) \%=20 \%$ P. $\mathrm{a}=10 \%$ compounded half yearly
$\mathrm{T}=$ 1year $=2$ half year
So,
$
\mathrm{CI}=7800\left[\left(1+\frac{10}{100}\right)^{2}-1\right]
$
$\Rightarrow \mathrm{CI}=7800 \times \frac{21}{100}=1638$ rupees.
Question 72:
In what time will Rs. 9,600 become Rs. 11,094 at $7 \frac{1}{2} \%$ p.a. compounded annually?
Correct Answer: 2
We know that:
$
\begin{aligned}
&\text { Amount }=P\left(1+\frac{r}{100}\right)^{t} \\
&\Rightarrow 11094=9600\left(\frac{\left(\frac{15}{2}\right)}{100}\right)^{t} \\
&\Rightarrow \frac{11094}{9600}=\left(1+\frac{15}{200}\right)^{t} \\
&\Rightarrow \frac{1849}{1600}=\left(\frac{215}{200}\right)^{t}
\end{aligned}
$
$
\begin{aligned}
&\Rightarrow\left(\frac{43}{40}\right)^{2}=\left(\frac{43}{40}\right)^{t} \\
&\Rightarrow \mathrm{t}=2 \text { years }
\end{aligned}
$
Question 73:
A sum of Rs. 12,500 amounts to Rs.16,250 in 4 years at simple interest per annum. If the interest rate is increased by $2.5 \%$ per annum, then the increased amount for the same period is:
Correct Answer: 1
Given:
Simple interest $=16250-12500=3750$ Rs.
Time $=4$ years
We know that:
$
\begin{aligned}
&\text { Simple interest }=\frac{P \times R \times T}{100} \\
&\Rightarrow 3750=\frac{12500 \times R \times 4}{100} \\
&\Rightarrow R=\frac{3750 \times 100}{12500 \times 4} \\
&\Rightarrow R=7.5 \%
\end{aligned}
$
New rate of interest $=7.5+2.5=10 \%$
Therefore, increased amount for the same period $=12500+\frac{12500 \times 10 \times 4}{100}=12500+5000=$ 17500 Rs.
MATHSMIRROR SOLUTION
Increased amount for the same period $=16250+\frac{12500 \times 2.5 \times 4}{100}=16250+1250=$ 17500 Rs.
Question 74:
Ram and Dipti each invested a sum of ₹ 8000 for a period of two years at $30 \%$ compound interest per annum. However, while for Ram the interest was compounded annually, for Dipti it was compounded every eight months. How much more will Dipti receive as interest compared to Ram at the end of the two-year period?
Correct Answer: 4
Interest received by $\mathrm{Ram}=$
$
\begin{aligned}
&8000\left(1+\frac{30}{100}\right)^{2}-8000 \\
&=8000 \times \frac{13}{10} \times \frac{13}{10}-8000 \\
&=13520-8000 \\
&=5520 \text { rupees }
\end{aligned}
$
For Dipti, Rate $=\frac{30}{12} \times 8=20 \%$ per 8 -months
Time $=2$ years $=3$ cycles of 8 months each
So, Interest Received by Dipti $=8000$
$
\left(1+\frac{20}{100}\right)^{3}-8000
$
$=8000 \times \frac{6}{5} \times \frac{6}{5} \times \frac{6}{5}-8000$
$=13824-8000$
$=5824$
Hence, Required Difference $=5824-5520=$ 304 rupees
Question 75:
Kritika lends ₹ 64000 to Nidhi for a year at $25 \%$ interest per annum, compounded half yearly. Find the interest that has to be paid by Nidhi.
Correct Answer: 2
$R=\frac{25}{2}=12 \frac{1}{2} \%$ $=\frac{1}{8}$ per half year
$\mathrm{T}=1$ year $=2$ cycles of half year
So, Interest paid by Nidhi =
$\Rightarrow$ Total Interest $=8000+8000+1000=$
17000 rupees
Question 76:
Kavita has deposited ₹ 4000 with the bank for two years at $6.25 \%$ simple interest per annum. What will be the total amount that Kavita will receive at the end of the two-year term?
Correct Answer: 4
$\begin{aligned} \text { SI received by Kavita } &=\frac{4000 \times 6.25 \times 2}{100} \\ &=500 \text { rupees } \end{aligned}$
So, Amount received by Kavita $=4000+500$ $=4500$ rupees
Question 77:
A farmer borrowed Rs.1,32,000 from a money lender to do cultivation in his field. The rate of interest is $12.5 \%$ per annum compounded annually. At the end of two years, he cleared his loan by paying Rs.1,07,062.50 and his scooter. The cost (in Rs.) of the scooter is:
Correct Answer: 3
We know that:
$
\begin{aligned}
&\text { Amount }=P\left(1+\frac{r}{100}\right)^{t} \\
&=132000\left(1+\frac{12.5}{100}\right)^{2} \\
&=132000\left(\frac{112.5}{100}\right)^{2} \\
&=132000 \times \frac{9}{8} \times \frac{9}{8} \\
&=167062.5 \mathrm{Rs} .
\end{aligned}
$
Therefore, the price of the scooter $=167062.5-107062.5=Rs. 60000$
Hence, option C is correct.
Question 78:
6 copies of a book can be bought for a certain sum payable at the end of a year, and 7 copies of the same book can be bought for the same sum in cash money. What is the rate per annum of simple interest (correct to one decimal place)?
Correct Answer: 3
Let the cost price of one copy of a book be $x$ Rs.
The cost price of 6 copies of a book $=6 x$
The cost price of 7 copies of a book $=7 x$
Simple interest $=7 x-6 x=x$
We know that:
$
\begin{aligned}
&\text { Simple interest }=\frac{P \times R \times T}{100} \\
&\Rightarrow \mathrm{X}=\frac{(6 x) \times R \times 1}{100} \\
&\Rightarrow \mathrm{R}=\frac{100 x}{6 x} \\
&\Rightarrow \mathrm{R}=16.7 \%
\end{aligned}
$
Therefore, the rate per annum of simple interest is $16.7 \%$
Question 79:
The interest, compounded annually, on a sum of Rs.3,240 after two years is Rs.370. What is the rate of interest, correct up to two decimal places?
Correct Answer: 3
Given:
Sum $=$ Rs. 3240 and Compound Interest $=$ Rs. 370 and Time $=2$ years
Compounded Sum $=\operatorname{Sum} \times(1+R)^{\top}$
$
\Rightarrow 3240+370=3240 \times(1+R)^{2}
$
$\Rightarrow(1+R)^{2}=\frac{3610}{3240}$
$\Rightarrow(1+R)^{2}=1.1142$
$\Rightarrow(1+R)=\sqrt{1.1142}$
$\Rightarrow 1+R=1.0556$
$\Rightarrow R=1.0556-1$
$
\Rightarrow R=.0556 \text { or } 5.56 \%
$
Hence, option C is the correct answer.
Question 80:
A certain sum was invested on simple interest for a period of seven years. During the period of the sixth and the seventh years combined, the interest earned was Rs.292. If the maturity amount is Rs.3,942, then what is the rate percentage of the interest?
Correct Answer: 1
Maturity amount = Rs. 3942
A combined interest in the sixth and the seventh years $=$ Rs. 292
Therefore, one year interest $=292 / 2=$ Rs. 146
7 years interest $=7 \times 146=$ Rs. 1022
Sum invested $=3942-1022=$ Rs. 2920
Rate of interest $=\frac{\text { Interest }}{\text { Sum }} \times 100=\frac{146}{2920} \times 100=5 \%$
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