Find the compound interest on Rs. 5000 in 2 years at 4% per annum, the interest being compounded half yearly.
R 412.16
R 312.16
R 400.16
R 420.16
Here, Principal P = Rs. 5000
Rate R = 4% pa
Time n = 2 years
Now according to the formula,
$\text { Amount } =\mathrm{P}\left(1+\frac{R}{2 \times 100}\right)^{2 n}=5000\left(1+\frac{4}{200}\right)^4$
$ =\left(5000 \times \frac{51}{50} \times \frac{51}{50} \times \frac{51}{50} \times \frac{51}{50}\right)=\left(\frac{51 \times 51 \times 51 \times 51}{1250}\right)$
$=\mathrm{R} 5412.16$
$\therefore Compound Interest = R (5412.16 – 5000) = R 412.16$
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Ruchi invested Rs. 1600 at the rate of compound interest for 2 years. She got Rs. 1764 after the specified period. Find the rate of interest.
5%
3%
7%
10%
Here, $\mathrm{P}=\mathrm{R} 1600, n=2$ years, $\mathrm{A}=\mathrm{R} 1764$
Now, according to the formula,
$ \text { Amount }=\mathrm{P}\left(1+\frac{R}{100}\right)^n$
$1764=1600\left(1+\frac{R}{100}\right)^2$
$\Rightarrow \quad \frac{1764}{1600}=\left(\frac{100+R}{100}\right)^2 \quad \Rightarrow \quad\left(\frac{21}{20}\right)^2=\left(\frac{100+R}{100}\right)^2$
$\Rightarrow \quad \frac{100+R}{100}=\frac{21}{20} \quad \Rightarrow \quad 100+\mathrm{R}=\frac{21}{20} \times 100$
$\Rightarrow 100+R = 105$
$\therefore R = 105-100 = 5%$
Find the compound interest on Rs. 8000 at 4% per annum for 2 years compounded annually
R 652.80
R 452.80
R 652
R 552.80
Here, P = R 8000, R = 4%, Time = 2 years
Now, according to the formula,
$\text { Amount }=\mathrm{P}\left(1+\frac{R}{100}\right)^n=8000\left(1+\frac{4}{100}\right)^2=8000 \times \frac{26}{25} \times \frac{26}{25}=\mathrm{R} 8652.80$
∴ CI = R (8652.80 – 8000) = R 652.80
Find the effective rate of interest if the normal rate of interest is 10% p.a. and the interest is compounded every six months.
21.5%
10.25%
5.25%
10%
for this take 100 as principal
R = 10 % and half yearly rate will be 5 %
5+5+0.25 = 10.25
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Find the interest earned in the first year on Rs.400 at 20%p.a. compound interest, the interest being compounded half yearly.
Rs.42
Rs.72
Rs.84
Rs.144
Because the interest compound half yearly
When interest calculated half yearly rate will be half and time will be double.
P = 400, R = 20 % P.A , T = 1 year
40 + 40 + 4
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A person deposited a certain amount in a bank which is offering 10% p.a. compound interest for the first two years and for the next two years, each year the rate of interest is 10% points more than previous year. The value of his investment at the end of the 3rd year is Rs.4840 more than that at the end of the second year. Find the total amount received by the person at the end of the 4^{th}year.
Rs.37752
Rs 38572
Rs.38752
Cannot be determined
P (120/100) (110/100) = (110/100) – P (110/100) ^{2} = 4840
P (1.2) (1.21) – P (1.21) = 4840
P = 20000 Rs.
For the fourth year R% is 30 %
= 20000 x (1.3) x (1.2 ) x (1.2)
= 37752
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A man lent Rs. 25000 for one year under compound interest, to five persons. He lent Rs.5500 at 5% p.a. to the first person, Rs 4000 at 13/2 % p.a. to the second person, Rs.3500 at 11/2% p.a to the third person and Rs.7000 at 17/2% p.a. to the fourth person. At what rate of interest should he lend the remaining amount so that he gets an interest at 8% p.a. on the entire amount?
12.25%
12.75%
13.55%
14.05%
P [1+R/100] ^{T} = P1 [1+R1/100] ^{T} + P2[1+R2/100] ^{T} + P3 [1+R3/100] ^{T}
{25000 x 8 x 1}/100 = {5500 x 1 x 5}/ 20 +{ 4000 x 13 x 1 }/200 + {3500 x 1 x 11}/200
By solving this we get
R = 13.55 %
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A person invested half of the money he has at a rate of 10% p.a. compounded annually and the remaining half at a rate of 20% p.a simple interest. After 2 years he received a total of Rs.2610 from both the investments. How much will he receive after 3 years?
Rs.2300
Rs.2931
Rs.2642
Rs.2800
A person has invested half of money he has at C.I at 10 % and the other half at S.I at the rate of 20 % p.a for the 2 years
p/2 (1.1)^{2 }+ p/2 (1.4) = 2610
p = .5220/2.61 = 2000
So at the end of 3^{rd} year
2000/2 x (1.1)^{3} + 2000/2 (1.6 ) = 2931 Rs.
A person borrowed a sum of Rs.20000 at a rate of 20% p.a compounded annually for three years. But after two years he paid Rs.12800 and after 3rd year he cleared the remaining balance. How much did he pay at the end of the 3rd year?
Rs.18200
Rs 18700
Rs.19200
None of these
P = 20000
R = 20 %
Amount after 2 years = P [1+r/100]^{2}
20000 [ 1+20/100]^{2}
= 28800
He paid 12800 so remaining amount 28800 – 12800
= 16000
Amount after 3 years = 16000 [ 1+20/100]
=16000 x 6/5
=96000/5
= 19200 Rs.
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A person deposited a sum of Rs 10000 in a bank for a period of n_{1} years at a rate of 20% p.a compounded annually. The same person deposited a sum of Rs.11520 in other bank for a period of n_{2} years at a rate of 25% p.a. simple interest. The amounts received from the two banks are equal and the total amount is Rs.34560 Find n_{1 }and n_{2}.
n_{1} = 3, n_{2} = 2
n_{1} = 2, n_{2} = 2
n_{1} = 1, n_{2} = 3
cannot be determined
Rs. 1000 becomes 34560/2 = 17280 at 20 %
At C.I on n_{1} years 11520 becomes 17280 at 25 % S.I in n_{2} years
17280 = 10000 (1+20/100)^{n1}
17280 = 10000 (6/5)^{n1}
(1.2)n_{1} = (1.2)^{3}
n_{1} = 3 years
17280 – 11520 = 11520 x n2 x 25 / 100
= 5760 = 11520 x n2 x 25 / 100
n2 = 2
n = 3, n2 = 2
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