A person deposited a sum of of Rs 6000 in a bank at 5% per annum simple interest. Another person deposited Rs 5000 at 8% per annum compound interest. After two years, the difference of their interest will be ?
(a) Rs. 230
(b) Rs. 232
(c) Rs. 430
(d) Rs. 600
(e) Rs. 932
Solution: (b)
Principal (\(\displaystyle {{P}_{1}}\)) = Rs. 6000
Time (t) = 2 years
Rate % = 5%
Simple interest=\(\displaystyle \frac{{6000\times 5\times 2}}{{100}}\)
=Rs.600
Principal ((\(\displaystyle {{P}_{2}}\)) = Rs. 5000
Time (t) = 2 years
Rate % = 8%
2 year effective rate for Compound interest
\(\displaystyle =5000\times \frac{{16.64}}{{100}}\)
=832
Difference=832-600=Rs. 232
A man borrow Rs. 4000 at 15%, compound rate of interest. At the end of each year he pays back Rs. 1500. How much amount should be pay at the end of the third year to clear all his dues?
(a) Rs. 874.75
(b) Rs. 824.50
(c) Rs. 924.25
(d) Rs. 974.25
(e) None of these
Solution: (a)
Amount after 1st year
\(\displaystyle \begin{array}{l}=Rs.\left[ {4000\left( {1+\frac{{15}}{{100}}} \right)-1500} \right]\\=Rs.\left[ {4000\left( {\frac{{23}}{{20}}} \right)-1500} \right]\\=Rs.\left[ {4600-1500} \right]\\=Rs.3100\end{array}\)
Amount after 2nd year
\(\displaystyle \begin{array}{l}=Rs.\left[ {3100\left( {1+\frac{{15}}{{100}}} \right)-1500} \right]\\=Rs.\left[ {3100\left( {\frac{{23}}{{20}}} \right)-1500} \right]\\=Rs.\left[ {3565-1500} \right]\\=Rs.2065\end{array}\)
Amount after 3rd year
\(\displaystyle \begin{array}{l}=Rs.\left[ {2065\left( {1+\frac{{15}}{{100}}} \right)-1500} \right]\\=Rs.\left[ {2065\left( {\frac{{23}}{{20}}} \right)-1500} \right]\\=Rs.\left[ {2374.75-1500} \right]\\=Rs.874.75\end{array}\)
Find the amount and the compound interest on Rs. 20000 for 1\(\displaystyle \frac{1}{2}\) years at 10% per annum compounded half-yearly.
Find the amount which Ram will get on ₹ 4096 if he gave it for 18 months at 12 \(\displaystyle \frac{1}{2}\) % per annum, interest being compounded half yearly
(a) Rs. 4613
(b) Rs. 4713
(c) Rs. 4813
(d) Rs. 4913
(e) None of these
Solution: (d)
Amount= \(\displaystyle =P\times {{\left( {1+\frac{r}{{100}}} \right)}^{n}}\)
P = ₹ 4096
n = 18 months = 1\(\displaystyle \frac{1}{2}\) years
R = 12\(\displaystyle \frac{1}{2}\)% p.a. compounded half-yearly
For calculation of Compound Interest (C.I.) compounded half-yearly, we will take the interest rate as half of 12 \(\displaystyle \frac{1}{2}\)% i.e, (25/2) ÷ 2 = 25/4 % and ‘n’ = 3 (Since, 18 ÷ 6 = 3)
Amount= \(\displaystyle =P\times {{\left( {1+\frac{r}{{100}}} \right)}^{n}}\)
\(\displaystyle \begin{array}{l}=4096\times {{\left( {1+\frac{{25}}{{4\times 100}}} \right)}^{3}}\\=4096\times {{\left( {\frac{{425}}{{400}}} \right)}^{3}}\\=4096\times {{\left( {\frac{{17}}{{16}}} \right)}^{3}}\\=4096\times \frac{{17}}{{16}}\times \frac{{17}}{{16}}\times \frac{{17}}{{16}}\\=Rs.4913\end{array}\)
What is the compound interest on Rs. 20,000 at 10 percent per annum for 2 years and 73 days?
(a) Rs. 4684
(b) Rs. 4732
(c) Rs. 4830
(d) Rs. 4950
(e) None of these
Solution: (a)
Sum(P)=Rs. 20,000
Rate of interest (R)=10%
73 days=73/365=1/5 years. (Assuming 1 year=365 days)
Period (N)=2 years and 73 days=2 1/5 years
First
Find the amount for 2 years using compound interest formula
Amount= \(\displaystyle =P\times {{\left( {1+\frac{r}{{100}}} \right)}^{n}}\)
\(\displaystyle \begin{array}{l}=20000\times {{\left( {1+\frac{{10}}{{100}}} \right)}^{2}}\\=20000\times {{\left( {\frac{{11}}{{10}}} \right)}^{2}}\\=20000\times \frac{{11}}{{10}}\times \frac{{11}}{{10}}\\=Rs.24200\end{array}\)
Next
On this amount calculate the simple interest for 1/5 years at 10% interest and the amount
P=24200, R=10%, N=1/5
Amount= P+ \(\displaystyle \frac{{PNR}}{{100}}\)
Interest = \(\displaystyle \frac{{PNR}}{{100}}=\frac{{24200\times \frac{1}{5}\times 10}}{{100}}=484\)
Amount=24200+484=Rs. 24684
Compound interest=24684–20000=4684
Compound interest=Rs. 4684
Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually.
(a) Rs. 3109
(b) Rs. 3200
(c) Rs. 3181
(d)Rs. 3901
(e) None of these
Solution: (a)
Principal, P=Rs. 8000
Rate, R =15%
Time(n) =2 years 4 months =2+\(\displaystyle \frac{4}{12}\) years =2 \(\displaystyle \frac{1}{3}\)years
Amount for 2 years is given as
Amount= \(\displaystyle =P\times {{\left( {1+\frac{r}{{100}}} \right)}^{n}}\)
\(\displaystyle \begin{array}{l}=8000\times {{\left( {1+\frac{{15}}{{100}}} \right)}^{2}}\\=8000\times {{\left( {\frac{{23}}{{20}}} \right)}^{2}}\\=8000\times \frac{{23}}{{20}}\times \frac{{23}}{{20}}\\=Rs.10580\end{array}\)
Interest for \(\displaystyle \frac{1}{3}\) years is given as
Interest =\(\displaystyle \frac{{PNR}}{{100}}\) =\(\displaystyle \frac{{10580\times \frac{1}{3}\times 15}}{{100}}=529\)
Total amount for 2\(\displaystyle \frac{1}{3}\)years =10580+529=Rs. 11109.
\(\displaystyle \Rightarrow \)Compound Interest= Total Amount – Principal = Rs. (11109 − 8000) = Rs. 3109.
