1. Calculate the difference between the simple
interest and the compound interest on 4,000
in 2 years at 8% per annum compounded yearly.
Answers
Answer:
Step-by-step explanation:
Principal (P) = Rs.4000
Rate (R) = 8%
Time (T) = 2years
\rm Simple \: Interest\: (SI) = \dfrac{PTR}{100}SimpleInterest(SI)=
100
PTR
\rm SI= \dfrac{4000 \times 2 \times 8}{100}SI=
100
4000×2×8
\rm SI= 40 × 16SI=40×16
\rm SI= 640SI=640
\rm \therefore Simple\: Interest= Rs.640∴SimpleInterest=Rs.640
Now, Compound Interest (CI) = Amount - Principal
\rm Amount = P \bigg(1 + \dfrac{r}{100}\bigg)^{n}Amount=P(1+
100
r
)
n
\rm \dashrightarrow CI = \bigg[P \bigg(1 + \dfrac{r}{100}\bigg)^{n}\bigg] - P⇢CI=[P(1+
100
r
)
n
]−P
\rm \dashrightarrow CI = \bigg[4000 \bigg(1 + \dfrac{8}{100}\bigg)^{2}\bigg] - 4000⇢CI=[4000(1+
100
8
)
2
]−4000
\rm \dashrightarrow CI = \bigg[4000 \bigg(\dfrac{108}{100}\bigg)^{2}\bigg] - 4000⇢CI=[4000(
100
108
)
2
]−4000
\rm \dashrightarrow CI = \bigg[4000 \times \bigg(\dfrac{27}{25}\bigg)^{2}\bigg] - 4000⇢CI=[4000×(
25
27
)
2
]−4000
\rm \dashrightarrow CI = \bigg[4000 \times \dfrac{27 \times 27}{25 \times 25}\bigg] - 4000⇢CI=[4000×
25×25
27×27
]−4000
\rm \dashrightarrow CI =4665.6 - 4000⇢CI=4665.6−4000
\rm \dashrightarrow CI =665.6⇢CI=665.6
\rm \therefore Compound \: Interest= Rs.665.6∴CompoundInterest=Rs.665.6
The difference between Simple Interest and Compound Interest
= 665.6 - 640
= 25.6
The difference between Simple Interest and Compound Interest is Rs 25.60
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hope it helps you