Question

The difference between compound interest and simple interest at the same rate on 5000 for 2 years is Rs. 72 . The rate of interest per annum is ? A) 6% B) 8% C) 10% D) 12%

Answer 1

Gɪᴠᴇɴ :-

• The difference between compound interest and simple interest at the same rate on 5000 for 2 years is Rs. 72 .

Tᴏ Fɪɴᴅ :-

• The rate of interest per annum is ?

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ :-

The Difference between compound interest and simple interest on the same sum P , with Rate as R% and Time Equals to 2 Years is :- (P * R²)/(100)²

Sᴏʟᴜᴛɪᴏɴ :-

→ Principal = Rs.5000

→ D = Rs.72

→ Time = 2 Years.

→ Rate = Let R%.

Putting values in Above Told Formula Now, we get :-

→ 72 = (5000 * R²)/(100*100)

→ 72 = (5 * R²) / 10

→ 72 = (R²/2)

→ 72 * 2 = R²

→ R² = 144

→ R² = 12 * 12

→ R² = (12)²

→ R = 12% (Ans.)

Hence, The Required Rate of interest is 12% Per Annum.

Answer 2

Answer:

option (D) 12%

Step-by-step explanation:

S.I. = ( 5000 × r/100× 2) = (100r).

C.I. = [5000 × ( 1+ r/100)^2-5000]

= { 5000 × [1+r/100)^2 -1 ] }

= [ 5000× ( r^2/10000+r/50)]

= 5000(r^2+200r) /10000 = ( r^ / 2 + 100r)

(C.I.) - ( S. I) = (r^2/2+100r) - (100r) = r^2/2.

so, r^2/2 = 72=> r^2 = 144 => r = √ 144 = 12.

Hence, rate = 12% p.a. ( ans)

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