Exercise : Compound Interest - General Questions
✔ Compound Interest -
General Questions
1.
Find the Compound Interest (CI) on $1,000 for 2 years at 10% per annum compounded annually.
View Answer
Answer: Option A
Explanation:
Explanation:
Using the formula \(A = P(1 + R/100)^T\), we get \(A = 1000(1.1)^2 = 1210\). The Compound Interest is \(CI = A - P = 1210 - 1000 = 210\).
2.
What will be the amount if $5,000 is invested for 3 years at 5% Compound Interest?
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Answer: Option A
Explanation:
Explanation:
Using \(A = P(1 + R/100)^T\), we have \(A = 5000(1.05)^3 = 5000 \times 1.157625 = 5788.13\).
3.
Find the Compound Interest on $2,000 for 1 year at 10% per annum compounded half-yearly.
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Answer: Option A
Explanation:
Explanation:
When compounded half-yearly, the rate is halved (\(R = 5%\)) and the time is doubled (\(T = 2\) half-years). \(A = 2000(1.05)^2 = 2205\). \(CI = 2205 - 2000 = 205\).
4.
At what rate % per annum will \(1,000 amount to \)1,331 in 3 years?
View Answer
Answer: Option A
Explanation:
Explanation:
Using the ratio \(A/P = (1 + R/100)^T\), we get \(1331/1000 = (1 + R/100)^3\). This simplifies to \(1.1^3 = (1 + R/100)^3\), so \(1 + R/100 = 1.1\), which means \(R = 10%\).
5.
In how many years will \(800 amount to \)926.10 at 10% per annum compounded semi-annually?
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Answer: Option A
Explanation:
Explanation:
Rate \(R = 5%\) per half-year. \(926.10 / 800 = (1.05)^n \implies 1.157625 = (1.05)^n\). Solving for \(n\), we get \(n = 3\) half-years, which is \(1.5\) years.
6.
The difference between Simple Interest (SI) and Compound Interest (CI) on a certain sum for 2 years at 5% is $25. Find the sum.
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Answer: Option A
Explanation:
Explanation:
The formula for the difference for 2 years is \(D = P(R/100)^2\). So, \(25 = P(5/100)^2 \implies 25 = P(1/400) \implies P = 10,000\).
7.
A sum of money at Compound Interest doubles itself in 5 years. In how many years will it become 8 times itself?
View Answer
Answer: Option A
Explanation:
Explanation:
If it becomes \(2^1\) times in 5 years, it will become \(2^3\) (8 times) in \(3 \times 5 = 15\) years.
8.
A sum amounts to $1,352 in 2 years and $1,406.08 in 3 years at Compound Interest. Find the rate of interest.
View Answer
Answer: Option A
Explanation:
Explanation:
The interest for the 3rd year is the interest on the amount at the end of the 2nd year. \(R = \frac{1406.08 - 1352}{1352} \times 100 = 4%\).
9.
Find the Compound Interest on $10,000 for 1 year at 20% per annum compounded quarterly.
View Answer
Answer: Option A
Explanation:
Explanation:
Quarterly rate \(R = 20/4 = 5%\). Time \(T = 4\) quarters. \(A = 10000(1.05)^4 = 12155.06\). \(CI = 12155.06 - 10000 = 2155.06\).
10.
A sum of money amounts to $6,690 after 3 years and $10,035 after 6 years at Compound Interest. Find the sum.
View Answer
Answer: Option A
Explanation:
Explanation:
The growth factor for 3 years is \(10035 / 6690 = 1.5\). Therefore, the principal \(P\) is \(6690 / 1.5 = 4,460\).