Tag: compounding interest non-annually

Questions Related to compounding interest non-annually

Choose the most appropriate option.
The value of a machine depreciates every year at the rate of $10\%$ on its value at the beginning of that year. If the present value of the machine is Rs. $729$, its worth three years ago was?

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. Rs. $947.70$

  2. Rs. $1,000$

  3. Rs. $750.87$

  4. Rs. $800$

Show answer
Correct Option: B
Explanation:

$P\left(1-\dfrac{10}{100}\right)^3=729$


$\Rightarrow$  $P\times\dfrac{90}{100}\times\dfrac{90}{100}\times\dfrac{90}{100}=729$

$\Rightarrow$  $P\times\dfrac{729}{10\times100}=729$

$\Rightarrow$  $P=\dfrac{729\times1000}{729}$

$\Rightarrow$  $P=Rs.1000$ 

$\therefore$  The value of machine $3$ years ago was $Rs.1000$

Find the amount of Rs 12000 after 2 years compounded annually the rate of interest being 5 % pa during the first year and 6% pa during the second year also find the compound interest?

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. Rs 1356

  2. Rs 1200

  3. Rs 1256

  4. Rs None of these

Show answer
Correct Option: A
Explanation:

P=Rs.12000,Time=2 Years,Rate=5% and 6%
$A=P\left(1+\frac{R}{100}\right)^T$
$\Rightarrow 12000\left(1+\frac{5}{100}\right)\left(1+\frac{6}{100}\right)$
$\Rightarrow 12000\times \frac{105}{100}\times \frac{106}{100}$
$\Rightarrow 13356  Rs$
$C.I=A-P$
$\Rightarrow 13356-12000=1356  Rs.$

A sum of money at CI amounts to thrice itself in $3$ years. In how many years will it be $9$ times itself?

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $18$

  2. $12$

  3. $6$

  4. $3$

Show answer
Correct Option: C
Explanation:

$\Rightarrow$ Let the sum = $Rs.x$.

$\Rightarrow$  Then we have $3x=x(1+\dfrac{r}{100})^3$
$\Rightarrow$  By squaring both the sides,
$\Rightarrow$  $9x^2=x^2(1+\dfrac{r}{100})^6$
$\therefore$   The sum x will be 9 times in $6\, years.$

A man borrowed Rs.$60,000$ for $2$ years at $8$ % per year compound interest. 

Calculate the final amount at the end of the second year.

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. Rs. $68,984$

  2. Rs. $69,744$

  3. Rs. $69,910$

  4. Rs. $69,984$

Show answer
Correct Option: D
Explanation:

$\Rightarrow$  $P=$Rs.$60000,\,T=2\,$years and $R=8\%$


$\Rightarrow$  $A=P(1+\dfrac{R}{100})^T$

$\Rightarrow$  $A=60000\times (1+\dfrac{8}{100})^2$

$\Rightarrow$  $A=60000\times (\dfrac{27}{25})^2$

$\Rightarrow$  $A=60000\times \dfrac{729}{625}$

$\therefore$     $A=$Rs. $69,984.$

What amount will sum up to Rs. $6,6550$ at $10$% p.a. in C.I. in $3$ years?

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $40000$

  2. $50000$

  3. $60000$

  4. $70000$

Show answer
Correct Option: B
Explanation:
$\Rightarrow$  Here, $A=Rs.66550\,R=10\%$ and $T=3\,years$
$\Rightarrow$  $A=P(1+\dfrac{R}{100})^T$

$\Rightarrow$  $66550=P\times (1+\dfrac{10}{100})^3$

$\Rightarrow$  $66550=P\times (\dfrac{11}{10})^3$

$\therefore$   $P=\dfrac{66550\times 1000}{1331}=Rs.50000$

A sum of Rs. $8,000$ is invested for $3$ years at $10 \%$ per annum compound interest. Calculate the interest for the second year.

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $440$

  2. $880$

  3. $330$

  4. $800$

Show answer
Correct Option: B
Explanation:

Given, $P=$ Rs. $8,000,\,R=10\%$.

Interest for second year $=$ $P\times \dfrac{R}{100}\times \left (1+\dfrac{R}{100}\right)$
$=$ $8000\times \dfrac{10}{100}\times \left (1+\dfrac{10}{100}\right)$
$=$ $800\times \dfrac {11}{10}$
Therefore, interest for second year $=$ Rs. $880.$

In what time will Rs, $15,000$ yield Rs. $4965$ as compound interest at $10$% per year compounded annually?

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $3$ years

  2. $2$ years

  3. $1$ years

  4. $4$ years

Show answer
Correct Option: A
Explanation:

Interest for the first year 

$=\cfrac{1500\times 10\times 1}{100}$
$=$ Rs $1500$
Amount after the first year $=$ Rs $15000+1500$
$=$ Rs $ 16500$ 
Interest for the second year
$=$ $\cfrac{16500\times 10\times 1}{100}$
$=$ Rs $1650$
Amount after the third year 
$=$ $\cfrac{18150\times 10\times 1}{100}$
$=$ Rs $1815$
Final amount $= $ Rs $18150+1815$
$=$ Rs $19965$
Compound interest $=$ Rs $19965-15000$
 $=$ Rs $4965$
Required time $= 3$ years

Find the compound interest on Rs. $70,000$ for $2$ years, compounded annually at $10\%$ per annum.

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $14,400$

  2. $14,700$

  3. $14,300$

  4. $14,100$

Show answer
Correct Option: B
Explanation:

Here,$P=$ Rs $7000$ , $R=10\%p.a$

interest for the first year $=\cfrac{P\times R\times T}{100}$
$=\cfrac{7000\times 10\times 1}{100}$
$=$ Rs $7000$
The amount after the first year $=$ Rs $77000$
Principal for the second year $=$ Rs $77000$
Interest for the second year $=$ Rs $\cfrac{77000\times 10\times 1}{100}$
$=$ Rs $7700$
The final amount $=$ Rs $77000$ + Rs $7700$
$=$ Rs $84700$
Compound interest $= $ Rs $84700 -70000$
$=$ Rs $14700$
                                                 


A finance company declares that, with compound interest rate, a sum of money deposited by anyone will become $8$ times in three years. if the same amount is deposited at the same compound-rate of interest, then in how many years it will become $128$ times?

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $4$

  2. $5$

  3. $6$

  4. $7$

Show answer
Correct Option: D
Explanation:

In three years.a sum of money deposited by anyone will become $=2^3=8$times

Therefore , to make sum of money $128$ times , then $2^7=128$, it will occcur in $7$ years.

What sum of money will amount to Rs. $63,888$ in three years at $10$% per annum compounded yearly?

mathematics and statistics compound interest [using formula] compounding interest annually compouding interest compounding interest non-annually

  1. $50,000$

  2. $48,000$

  3. $46,000$

  4. $40,000$

Show answer
Correct Option: B
Explanation:

$A=P(1+\cfrac{r}{100})^n$

$\implies 63888=P(1+\cfrac{10}{100})^3\ \implies P=48,000$
Hence sum$=Rs.48,000$.