Anamika took a loan of R40,000 from a branch of a bank. The rate of interest is 5% per annum. Find the difference in amounts she would be paying after1 years if the interest is compounded annually and compounded half-yearly.
Answers
Step-by-step explanation:
Since, the amount formula in compound interest is,Since, the amount formula in compound interest is,
A=P(1+\frac{r}{n})^{nt}A=P(1+
n
r
)
nt
Where,
P = principal amount,
r = rate of interest annually,
n = number of periods in a year,
t = number of years,
If P = 40000, r = 5% = 0.05,
Then, the difference in amount she would paying after 1½ years if the interest is compounded annually and compounded half yearly.
d=40000(1+\frac{0.05}{2})^3-40000(1+\frac{0.05}{1})^\frac{3}{2}d=40000(1+
2
0.05
)
3
−40000(1+
1
0.05
)
2
3
=40000((1.025)^3-(1.05)^\frac{3}{2})=40000((1.025)
3
−(1.05)
2
3
)
\approx 38.43\text{ rupees}≈38.43 rupees
A=P(1+\frac{r}{n})^{nt}A=P(1+
n
r
)
nt
Where,
P = principal amount,
r = rate of interest annually,
n = number of periods in a year,
t = number of years,
If P = 40000, r = 5% = 0.05,
Then, the difference in amount she would paying after 1½ years if the interest is compounded annually and compounded half yearly.
d=40000(1+\frac{0.05}{2})^3-40000(1+\frac{0.05}{1})^\frac{3}{2}d=40000(1+
2
0.05
)
3
−40000(1+
1
0.05
)
2
3
=40000((1.025)^3-(1.05)^\frac{3}{2})=40000((1.025)
3
−(1.05)
2
3
)
\approx 38.43\text{ rupees}≈38.43 rupees
Hope it helps
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