3.what is the difference of the CI and SI on rupees 16,000 at the rate of interest pipe percent per annum compounded half yearly for rupees 1½
4. on what sum of money will the difference between the simple and compound interest for 2 years at the rate of interest of 5% per annum compounded annually be equal to rupees 25?
5. a person invest a same amount of rupees 80000 in the to scheme 1 is based on the simple interest and scheme 2 is based on the compound interest compounded annually how much excess interest does the person and in the in the scheme 2.
6.a businessman invest same amount of two project with the same rate of interest 12% p.a. 450 1.5 years whereas the project one is based on the simple interest and project 2 is based on the compound interest compounded half yearly. if he and an excess interest of rupees 1377 in project 2 find the sum invested.
7. thethe simple interest on a sum for 2 years at 10% per annum is 1200 whereas the compound interest on the same sum for for the same period and rate is 1280 rupees what is the difference between the CI and SI for 3 years at the same rate of interest?
Answers
Answer:
For the first 2 years
S.I.=
100
P×N×R
⇒S.I.=
100
16,000×2×20
⇒S.I.=6,400
Amount = S.I. + P
⇒Amount=6,400+16,000
⇒Amount=22,400
Amount in the account at the end of the two years is Rs. 22,400.
For the remaining one year.
A=P(1+
2×100
r
)
n×2
⇒A=22,400(1+
200
20
)
2
⇒A=22,400(
10
11
)
2
⇒A=27,104
The total amount to be paid at the end of the three years is Rs. 27,104.
Let the principal be Rs. P
Given : R=5%,T=24 years
C.I. for 2 years =P(1+
100
5
)
2
−P
S.I. for 2 years =
100
P×5×2
=
10
P
∵ Difference between C.I. and S.P. = Rs. 25
P(1+
100
5
)
2
−P−
10
P
=25
400
441P
−
10
11P
=25
400
441P−440P
=25
P=10,000
Hence, the principle should be Rs. 10,000
Given
P=Rs.8,000
N=3years
R=10%
Simple Interest I=
100
PNR
So, Simple Interest in 3 years I=
100
8,000×3×10
=Rs.2,400
And Amount after "n" years of interest being compounded annually A=P(1+
100
R
)
n
So, Amount after 3 years of compound interest A=8,000×(1+
100
10
)
3
=8,000×1.1
3
=Rs.10,648
So, Compound Interest =A−P=Rs.10,648−Rs.8,000=Rs.2,648
And difference in CI and SI =Rs.2,648−Rs.2,400=Rs.248