What is the difference between the compound interest and simple interest on 8000 at 15% per annum for 2 year?

What will be the amount after 15 months on Rs 8000 at 12% per annum compounded 5 monthly?

1. Rs 1261
2. Rs 9261
3. Rs 9440
4. Rs 9200

Answer (Detailed Solution Below)

Option 2 : Rs 9261

Given:

Principal = Rs 8000

Rate = 12% per annum

Time = 15 Months

Rate will be compounded 5 monthly.

Formula Used:

\({\rm{A}} = {\rm{P}}{\left[ {1 + \frac{{\rm{r}}}{{100}}} \right]^n}\)

Concept Used:

15 Months is 3 terms of 5 months

12% is gained in 12 months, so in 5 months it will be 5%.

Calculation:

\({\rm{A}} = 8000{\left[ {1 + \frac{5}{{100}}} \right]^3}\)

⇒ A = (8000 × 21 × 21 × 21)/(20 × 20 × 20) = Rs 9261

∴ The Amount earned will be Rs 9261.

Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!

Disclaimer

The questions posted on the site are solely user generated, Doubtnut has no ownership or control over the nature and content of those questions. Doubtnut is not responsible for any discrepancies concerning the duplicity of content over those questions.

Given : P = Rs. 8,000, R = 5%, T = 2 years
For simple interest,

S.I. = `[ "P" xx "R" xx "T"]/100`

= `[8,000 xx 5 xx 2]/100`

= Rs. 800

For compound interest,

`"A" = "P"( 1 + r/100 )^n`

`"A" = 8,000( 1 + 5/100 )^2`

= `8,000 xx 21/20 xx 21/20`

= Rs. 8,820

C.I. = A - P
      = Rs. (8,820 - 8,000)
      = Rs. 820

Now, C.I. - S.I. = Rs. ( 820 - 800 ) = Rs. 20.
Thus, the difference between the compound interest and the simple interest is Rs. 20.

Solution

Principal(P)=Rs. 8000
Rate(R)=10% p.a.
Period(T)=3 years
∴ S.I for 3 years= PTR100=8000×10×3100
=Rs. 2400
Now, S.I. for 1st year = Rs.8000×10×1100
=80×10×1
Amount for the first year=P+S.I.
=Rs. 8000 + Rs. 800=Rs. 8800
Principal for the second year= Rs. 8800
Interest for the second year= 8800×10×1100
=Rs. 880
∴ Amount after second year= Rs. 8800 + Rs. 880
=Rs. 9680
Principal for the third year= Rs. 9680
Interest for the third year
= Rs.9680×10×1100=Rs.968
∴ C.I. for 3 years= Rs. 800+ Rs. 880+Rs. 968
∴ Difference between C.I. and S.I. for 3 years
=Rs. 2648-Rs. 2400 =Rs. 248

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Solution

The correct option is A: Rs.3109

Given: Principal, P=Rs.8000

Rate, R =15%

Time =2 years 4 months =2+(412) years =213 years

Amount for 2 years is given as

Amount, A=P(1+R100)t [∵t=time]

= Rs. [8000×(1+15100)2]

=Rs.(8000 ×2320× 2320

=10580

Interest for 13 years is given as

I=P×R×t100

=10580×15×13100

=Rs.529

Total amount for 213 years =10580+529=Rs.11109.

∴ Compound Interest, C.I.= Toatal Amount - Principal =Rs.(11109 −8000)= Rs.3109.

What is the difference between C.I and SI on 8000 at 15% per annum for 2 years?

What is the difference between the compound interest and simple interest on 8000 at 15% for 2 years?

What is the difference between compound interest and simple interest on 8000 at 15% per annum?

What is the difference between the compound interest and simple interest on Rupees 8000?