Question Detail

The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is

4 years
5 years
6 years
7 years

Answer: Option A

Explanation:

As per question we need something like following

\begin{aligned}
P(1+\frac{R}{100})^n > 2P \\
(1+\frac{20}{100})^n > 2 \\
(\frac{6}{5})^n > 2 \\
\frac{6}{5} \times \frac{6}{5} \times \frac{6}{5}\times\frac{6}{5} > 2

\end{aligned}

So answer is 4 years

1. Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quarterly

Rs 2520
Rs 2521
Rs 2522
Rs 2523

Answer: Option C

Explanation:

Please remember, when we have to calculate C.I. quarterly then we apply following formula if n is the number of years

\begin{aligned}
Amount = P(1+\frac{\frac{R}{4}}{100})^{4n}
\end{aligned}

Principal = Rs.16,000;
Time=9 months = 3 quarters;
Rate = 20%, it will be 20/4 = 5%

So lets solve this question now,

\begin{aligned}
Amount = 16000(1+\frac{5}{100})^3 \\
= 18522\\
C.I = 18522 - 16000 = 2522
\end{aligned}

2. Effective annual rate of interest corresponding to nominal rate of 6% per annum compounded half yearly will be

6.09%
6.10%
6.12%
6.14%

Answer: Option A

Explanation:

Let the amount Rs 100 for 1 year when compounded half yearly, n = 2, Rate = 6/2 = 3%

\begin{aligned}
Amount = 100(1+\frac{3}{100})^2 = 106.09
\end{aligned}

Effective rate = (106.09 - 100)% = 6.09%

3. Find the compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.

Rs. 610
Rs. 612
Rs. 614
Rs. 616

Answer: Option B

Explanation:

\begin{aligned}
Amount = [7500 \times (1+ \frac{4}{100})^2] \\
= (7500 \times \frac{26}{25} \times \frac{26}{25}) \\
= 8112 \\

\end{aligned}

So compound interest = (8112 - 7500) = 612

4. A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 840 in 4 years. The rate on interest per annum is.

Answer: Option B

Explanation:

S.I. on Rs 800 for 1 year = 40

Rate = (100*40)/(800*1) = 5%

5. The present worth of Rs.169 due in 2 years at 4% per annum compound interest is

Rs 155.25
Rs 156.25
Rs 157.25
Rs 158.25

Answer: Option B

Explanation:

In this type of question we apply formula
\begin{aligned}
Amount = \frac{P}{(1+\frac{R}{100})^n} \\
Amount = \frac{169}{(1+\frac{4}{100})^2} \\
Amount = \frac{169 * 25 * 25}{26*26} \\
Amount = 156.25
\end{aligned}