What would be the amount if interest is rupees 800 at 6% per year for 9 years

Last updated date: 27th Dec 2022

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Answer

Hint: If we have principal (P), rate (r), and time (t), then the value of the simple interest (S.I) is given as follows:
\[S.I=\dfrac{P\times r\times t}{100}\]

Complete step by step answer:
In the given question, we have been given P = Rs. 800, r = 5 % and t = 3 years. Now we know that if we have P, r and t, then the S.I is given as follows:
\[S.I=\dfrac{P\times r\times t}{100}......\left( i \right)\]
We will substitute the values of P, r and t in the equation (i) and we get,
\[S.I=\dfrac{800\times 5\times 3}{100}\]
On multiplying the terms of the numerator, we get
\[S.I=\dfrac{12000}{100}\]
On cancelling the zeros and simplifying it further, we get
S.I = Rs. 120
Hence, we get the value of S.I as equal to Rs. 120.
Therefore the correct option of this question is (a).

Note:Students have to be careful while multiplying the terms of the numerator as they might make a mistake, otherwise the calculation is quite easy. Also, they should remember that they do not have to substitute the value of rate by changing it from percentage as it has been already converted in the formula of simple interest (S.I). Simple interest is different from compound interest, so students must not get confused with both these concepts. They must read the question carefully and then apply the formula for simple interest.

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Stay updated with the Quantitative Aptitude questions & answers with Testbook. Know more about Interest and ace the concept of Simple Interest.

Latest Simple Interest MCQ Objective Questions

Simple Interest Question 1:

A man borrowed a loan of Rs. 12000 at simple interest and returned Rs. 16800 after 1 year, then what will be the simple interest on Rs. 8000 in 3 years at the same rate of interest?

1. Rs. 8650
2. Rs. 9800
3. Rs. 7600
4. Rs. 9600
5. None of the above/More than one of the above.

Answer (Detailed Solution Below)

Option 4 : Rs. 9600

Stay updated with the Quantitative Aptitude questions & answers with Testbook. Know more about Interest and ace the concept of Simple Interest.

Given:

The principal amount = Rs. 12000

Amount in 1 year = Rs.16800 

Formula used:

S.I = P × R × T /100

A = S.I + P 

Calculation:

Simple interest for 1 year = 4800

⇒ 4800 = 12000 × R/100

⇒ 40% = R

S.I for 3 years on 8000

S.I = P × R × T /100

⇒ 8000 × 40 × 3/100

⇒Rs. 9600 

∴ S.I for 3 years on 8000 is 9600 rupees

For 3 year = 3200 × 3 = 9600

∴ S.I for 3 years on 8000 is Rs.9600 

Simple Interest Question 2:

A sum of money at simple interest amounts to Rs. 850 in 4 years and Rs. 800 in 3 years. The sum is:

1. Rs. 650
2. Rs. 750
3. Rs. 720
4. Rs. 800
5. None of the above/More than one of the above.

Answer (Detailed Solution Below)

Option 1 : Rs. 650

Given:

Amount in 3 years = Rs. 800

Amount in 4 years = Rs. 850

Concept used:

In case of simple interest, the sum increases with a fixed proportion.

Calculation:

Interest of 1 year = 850 - 800

⇒ Interest of 1 year = Rs. 50

⇒ Interest of 3 years = Rs. 150

According to the question,

Principal = 800 - 150

⇒ Principal = Rs. 650

∴ The principal is Rs. 650.

Simple Interest Question 3:

The amount of interest earned in two years on a deposit of ₹10,000 at simple interest rate of 10% is

1. 1,000
2. 2,213
3. 2,000
4. 200

Answer (Detailed Solution Below)

Option 3 : 2,000

Given:

Principal = Rs. 10000

Time = 2 years 

Rate = 10%

Formula used:

Simple interest = (P × R × T)/100

Calculation:

Simple Interest = (10000 × 2 × 10)/100

⇒ Rs. 2000

∴ The simple interest is Rs. 2000.

Simple Interest Question 4:

Difference between compound interest and simple interest on Rs. 7200 for 2 years at x% per annum is Rs. 200. Find the value of x.

1. 15%
2. \(15\frac{1}{3}{\rm{\% }}\)
3. \(16\frac{2}{3}\%\)
4. 18%
5. None of the above

Answer (Detailed Solution Below)

Option 3 : \(16\frac{2}{3}\%\)

We know the formula for simple Interest,

⇒ SI = P × R × t/100

We know the formula for compound interest-

\(\Rightarrow {\rm{CI}} = \left[ {{\rm{P}}\left\{ {{{\left( {1 + \frac{{\rm{r}}}{{100}}} \right)}^{\rm{t}}} - 1} \right\}} \right]\)

Where, SI = Simple Interest, P = Principle, R = Rate of Interest, t = Time period, CI = Compound interest

Difference between compound interest and simple interest on Rs. 7200 for 2 years at x% per annum is Rs. 200.

\(\therefore 200 = 7200\left[ {{{\left( {1 + \frac{x}{{100}}} \right)}^2} - 1} \right] - \frac{{7200 × x × 2}}{{100}}\)

⇒ 72 × (10000 + x2 + 200x) – 720000 – 14400x = 20000

⇒ 720000 + 72x2 + 14400x – 720000 – 14400x = 20000

⇒ 72x2 = 20000

⇒ x2 = 20000/72 = 10000/36

\(\Rightarrow \;{\rm{x}} = \sqrt {\frac{{10000}}{{36}}} = \frac{{100}}{6} = 16\frac{2}{3}{\rm{\% }}\)

Difference = (P × r2)/1002

200 = (7200 × r2)/100 × 100

r2 = 20000/72 

rate of interest = 16(2/3)%

​

Simple Interest Question 5:

'A' lent ₹5000 to 'B' for 2 years and ₹3000 to 'C' for 4 years on simple interest at the same rate of interest and received ₹2200 in all from both of them as interest. The rate of interest per annum is-

1. 7%
2. \(7 \frac{1}{8} \%\)
3. 10%
4. 5%

Answer (Detailed Solution Below)

Option 3 : 10%

Given:

Principal of B = Rs. 5000 and Time for B = 2 years

Principal of C = Rs. 3000 and Time for C = 4 Years

Overall Interest on both = Rs. 2200

Concept Used:

Simple Interest S.I. = \(\frac{P\times R\times T}{100}\)

Calculation:

Let the rate of interest for both B and C be R%

According to the question,

S.I. of A = S.I. of B + S.I. of C

⇒ 2200 = \(\frac{5000 \times 2 \times R}{100}\) + \(\frac{3000 \times 4 \times R}{100}\)

⇒ 2200 = 100R + 120R

⇒ 2200 = 220R

⇒ R = 10%

∴ The rate of interest per annum is 10%.

Top Simple Interest MCQ Objective Questions

A sum of money at simple interest doubles in 10 years. In how many years, at the same rate, will it be tripled?

1. 30 years
2. 25 years
3. 20 years
4. 15 years

Answer (Detailed Solution Below)

Option 3 : 20 years

Given:

Amount = 2P

Time = 10 years

Formula used:

SI = (PRT/100) 

Amount = (PRT/100) + P

Calculation:

Amount = (PRT/100) + P

2P = (PR/10) + P 

⇒ P = (PR/10) 

⇒ R = 10%

According to the question, Amount = 3P

3P = (10PT/100) + P 

⇒ 2P = (PT/10)

⇒ T = 20 years

 ∴ Time taken to triple the amount is 20 years.

Time = 10 year

Hence, rate = Interest/Time = 100/10 = 10%

New interest = 3P - P = 2P = 200% of principle

∴ Time = Interest/Rate = 200/10 = 20 Years

Simple interest on a sum of money for 5 years is \(\frac{2}{5}\) times the principal, the rate for simple interest is 

1. 13%
2. \(12\frac{1}{3}\% \)
3. \(14\frac{1}{3}\% \)
4. \(8\% \)

Answer (Detailed Solution Below)

Option 4 : \(8\% \)

Let P = principal, R = rate of interest and N = time period

Simple interest = PNR/100

Given,

N = 5 years​

Then,

⇒ 2/5 × P = (P × R × 5)/100

⇒ R = 200/25

\(\therefore {\rm{\;}}R = 8 % \) %

The simple interest on a sum for 6 years is Rs. 29250. The rate of interest for the first 2 years is 7 percent per annum and for the next 4 years is 16 percent per annum. What is the sum?

1. Rs. 36600
2. Rs. 37500
3. Rs. 35400
4. Rs. 38300

Answer (Detailed Solution Below)

Option 2 : Rs. 37500

Given:

The simple interest for 6 years on a sum = 29250

Formula used:

\(SI\ =\ {P\ \times R\ \times T \over 100}\)     (Where SI = Simple interest, P = Principle, R = The rate, and T = The time)

Calculation:

Let us assume the sum be P

⇒ The simple interest for the first 2 years at a 7% rate = \(\ {P\ \times 7\ \times 2 \over 100}\ = {14P\over 100}\)

⇒ The simple interest for the next 4 years at a 16% rate = \(\ {P\ \times 16\ \times 4 \over 100}\ = {64P\over 100}\) 

⇒ The total simple interest = 29250

⇒ \({14P\over 100}\ +\ {64P\over 100}\ =\ 29250\)

\({78P\over 100}\ =\ 29250\)

⇒ By solving 

⇒ The required sum = P = 37500

∴ The required result will be 37500.

What is the simple interest on Rs. 32,000 at 8.5% per annum for period from 10th Feb., 2019 to 24th April, 2019?

1. Rs. 550
2. Rs. 555
3. Rs. 544
4. Rs. 540

Answer (Detailed Solution Below)

Option 3 : Rs. 544

Given:

Principle, P = Rs. 32,000

Rate, r = 8.5%

Time, t = (18 + 31 + 24) / 365 = 73 / 365 = 1 / 5 years

Concept used:

Simple Interest = (P × r × t) / 100

Calculation:

SI = (32,000 × 8.5 × 1 / 5) / 100

⇒ (32 × 85) / 5

⇒ 32 × 17

⇒ Rs. 544

A sum becomes Rs. 10650 in 5 years. and Rs. 11076 in 6 years. at simple interest. What is the sum?

1. Rs. 8946
2. Rs. 8740
3. Rs. 8520
4. Rs. 8800

Answer (Detailed Solution Below)

Option 3 : Rs. 8520

Concept Used:

In this type of question, number can be calculated by using the below formulae

Formula Used:

If a sum with simple interest rate, amounts to Rs. ‘A’ in y years. and Rs. ‘B’ in z years. then,

P = (A × z – B × y)/(z – y)

Calculation:

Using the above formulae, we have

⇒ P = (10650 × 6 – 11076 × 5)

⇒ P = Rs. 8520

∴ Required principal is Rs. 8520 

A sum becomes Rs. 10650 in 5 years. and Rs. 11076 in 6 years. at simple interest

Interest of 1 year = 11076 – 10650 = Rs. 426

Interest of 5 year = 426 × 5 = 2130

∴ Required principal = 10650 – 2130 = Rs. 8520

The amount becomes 12100 after 2 years and 13310 after 3 years, then find the rate of simple interest.

1. 10%
2. 12.5%
3. 15%
4. 8.5%

Answer (Detailed Solution Below)

Option 2 : 12.5%

Given:

The amount for 2 years = 12100

The amount for 3 years = 13310

Formula used:

Simple Interest = (Principal × rate × time)/100

Calculation:

Interest for 3rd year

⇒ 13310 – 12100 = 1210

Interest for 1 years = Rs. 1210

Principal = amount for 2 years – interest fo 2 years

Principal = 12100 – 2 × 1210 = 9680

1210 = (9680 × rate × 1)/100

⇒ rate = 12.5%

∴ The rate of interest is 12.5%.

A sum of Rs. 8250 gives simple interest of Rs. 2475 in 5 years. What will be the rate of interest per annum?

1. 7.5%
2. 8%
3. 6%
4. 10%

Answer (Detailed Solution Below)

Option 3 : 6%

GIVEN:

Principal = Rs. 8250

Interest = Rs. 2475

Time = 5 years

FORMULA USED:

Simple Interest = (Principal × Rate × time)/100

CALCULATION:

2475 = (8250 × R × 5)/100

∴ R = 6%

Ronit distributed sum of Rs. 50000 to his friend and his aunty at 5% and 5% for 6 and 4 year respectively. In the end Ronit got same amount form his friend and his aunty. Find the amount borrowed by his friend and his aunty.

1. Rs. 22000, Rs. 28000
2. Rs. 24000, Rs. 26000
3. Rs. 32000, Rs. 18000
4. Rs. 30000, Rs. 20000

Answer (Detailed Solution Below)

Option 2 : Rs. 24000, Rs. 26000

Given

Ronit distributed sum of Rs. 50000 to his friend and his aunty at 5% and 5% for 6 and 4 year respectively

Amount that he recieved from both of them was same.

Formula used

SI = (P × R × T) / 100

Where as, 

SI = Simple Interest

P = Principal

R = Rate

T = time period

Amount = Principal + SI

Calculation

Let Ronit's friend share be Rs.x then his aunty's share be Rs.(50000 - x)

⇒ A = P{1 + (R × T) / 100} = P{1 + (R × T) / 100} 

⇒ x{1 + (5 × 6) / 100} = (50000 - x){1 + (5 × 4) / 100}

⇒ x(130 / 100) = (50000 - x)(120 / 100)

⇒ 130x = 60,00,000 - 120x

⇒ 250x = 60,00,000

⇒ x = Rs. 24000

∴ Ronit's friend's share is Rs. 24000 and his aunty's share is Rs. 26000

If Amount is same then ratio of principal be

[1 /(100 + r1t1)]: [1 /(100 + r2t2)] ....

P1 : P2 = (1 / 100 + 5 × 6 ) : (1 / 100 + 5 × 4)

P1 : P2  = (1 / 130) : (1 / 120)

P1 : P2  = 12 : 13

(12 + 13) UNIT = Rs.50000

25 unit = 50000

1 unit = 2000

Friend's share = 12 × 2000 = Rs. 24000

His aunt's share = 50000 - 24000 = Rs. 26000

A certain sum amounts to ₹11760 in \(2\frac{1}{2}\) years at 9% p.a. simple interest. What will be the simple interest on the same sum for \(4\frac{2}{5}\) years at 15% p.a?

1. ₹6336
2. ₹6363
3. ₹6436
4. ₹6433

Answer (Detailed Solution Below)

Option 1 : ₹6336

Given:

Amount = Rs. 11760

Time = 2.5 years

Rate% = 9% p.a.

Formula used:

Simple interest = (Principal × time × rate)/100

Amount = Principal + simple interest

Calculation:

Let the principal be x

⇒ {x + (x × 2.5 × 9)/100} = 11760

⇒ 100x + 22.5x = 11760 × 100

⇒ 122.5x = 11760 × 100

⇒ x = 9600

According to question:

Time = \(4\frac{2}{5}\) = 22/5 years

Simple interest = {(9600 × 15 × 22)/(5 × 100)} = Rs. 6336

∴ the simple interest = Rs.6336

An equal amount of sum is invested in two different schemes for 2 years at simple interest with rates 14% p.a and 11% p.a. If the total interest after 2 years is Rs.2724, then find the sum invested on each scheme.

1. Rs.4688
2. Rs.5448
3. Rs.4680
4. Rs.5746

Answer (Detailed Solution Below)

Option 2 : Rs.5448

Given:

Sum is invested for 2 years at the rates 14% and 11%

Total sum of S.I = Rs.2724

Concept used:

S.I = (P × R × T)/100

Calculation:

Let the sum be Rs.x

Then, S.I for 2 years @ 14% = 28x/100

Also, S.I for 2 years @ 11% = 22x/100

Total interest = 28x/100 + 22x/100 = 50x/100

As per the question,

50x/100 = 2724

⇒ x = 2724 × 100/50

⇒ x = 5448

∴ The sum is Rs.5448