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July 15, 2023
On this page we have discussed Compound Interest formulas, definition with examples.
Compound Interest in MathsCompound interest is a concept in mathematics and finance that refers to the interest earned or paid on an initial amount of money, called the principal, as well as any accumulated interest from previous periods. Unlike simple interest, where interest is only calculated based on the initial principal, compound interest takes into account both the initial amount and the interest earned over time.
Formula of Compund Interest (CI) = P (1+ \mathbf{\frac{r}{100n}})^{nT} – P
Formula of Amount = CI +P
= P (1+ \mathbf{\frac{r}{100n}})^{nT} – P + P
Here, P = Principal
r = rate of interest
T = the number of years the amount is deposited or borrowed for.
n= the number of times that interest is compounded per unit ‘t’.
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Question 1 . Find the amount on Rs 16000 for 3 year at 5% per annum compounded annually n.
[A] Rs. 18562
[B] Rs. 18550
[C] Rs. 18952
[D] Rs. 18552
Solution : According to the formula of Compound Interest
Amount = P (1+ \mathbf{\frac{r}{100}})^{n}
Amount = 16000 (1+ \mathbf{\frac{5}{100}})^{3}
Amount = 16000 (1+ \mathbf{\frac{1}{20}})^{3}
Amount = 16000 (\mathbf{\frac{21}{20}})^{3}
Amount =18552
Correct Option: D
Question 2 . Find the compound interest on Rs. 10,000 at 20% per annum for 5 years 4 months, compounded annually is :
[A] Rs. 16600
[B] Rs. 16544
[C] Rs. 15644
[D] Rs. 16500
Solution : According to the Formula of Compound Interest ,
CI = P (1+ \mathbf{\frac{r}{100}})^{n} – P
y = 53800
Correct Option: 53800
[A] 9
[B] 1
[C] 2
[D] 3
Solution: As C.I for the 1st year = S.I
Interest for 1st year = 73000*\frac{10}{100}
= 7200 Rs
As interest on interest is C.I
Interest for the 2nd year = 7200 + 7200*\frac{10}{100}
= 7200 + 720 = 7920
Interest for the 3rd year = 7920 + 7920\frac{10}{100}
= 7920 + 792 = 8712
Total interest at the end of 3 years = 7200 + 7920 + 8712
= 23832
Therefore t = 3
Correct Option= 3
Question 5 . The Compound Interest on a certain amount at a certain rate of interest, for the 7th and 8th year, was Rs 2180 and Rs 2659.6 respectively. Find the rate of interest per annum. [A] 3 [B] 12 [C] 22 [D] 28
Solution: Using interest on interest is C.I Let r be rate of interest 2180 + 21.8r = 2659.6 21.8r = 2659.6 – 2180 r = 22
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