Question

Q3. एक राशि पर 3 वर्ष के अंत में 15% वार्षिक दर से उपचित चक्रवृद्धि ब्याज रु 6500.52 है। राशि कितनी है ? answer ​

Answer 1

Answer

Amount = Rs. 18,980.52

Explanation

Given

Compound Interest = Rs 6500.52

Time = 3 years

Rate = 15%

To find

Amount

Knowledge required

Formula of compound Interest :-

⠀⠀⠀C.I. = P[1 + r/100]ⁿ - P

Formula to calculate amount, when compound interest and principal is given.

⠀⠀⠀Amount = C.I. + Principal

where,

P = Principal

r = rate

n = time

Solution

Firstly, we will find the principal by using the formula of compound interest. Then by substituting the value of principal and compound interest in the formula of amount we will find its value.

⠀⠀⠀⇒ C.I. = P[1 + r/100]ⁿ - P

⠀⠀⠀⇒ 6500.52 = P[1 + 15/100]³ - P

⠀⠀⠀⇒ 6500.52 = P[1 + 3/20]³ - P

⠀⠀⠀⇒ 6500.52 = P[(20 + 3)/20]³ - P

⠀⠀⠀⇒ 6500.52 = P[23/20]³ - P

⠀⠀⠀⇒ 6500.52 = P[12167/8000] - P

⠀⠀⠀⇒ 6500.52 = 12167/8000P - P

⠀⠀⠀⇒ 6500.52 = (12167P - 8000P)/8000

⠀⠀⠀⇒ 6500.52 = 4167/8000 P

⠀⠀⠀⇒ 6500.52 × 8000/4167 = P

⠀⠀⠀⇒ 650052/100 × 8000/4167 = P

⠀⠀⠀⇒ 650052 × 80/4167 = P

⠀⠀⠀⇒ Dividing 650052 and 4167 by 3.

⠀⠀⠀⇒ 216,684 × 80/1389 = P

⠀⠀⠀⇒ Dividing 216,684 and 1389 by 3.

⠀⠀⠀⇒ 72,228 × 80/463 = P

⠀⠀⠀⇒ [463 × 156 = 72,228]

⠀⠀⠀⇒ 156 × 80 = P

⠀⠀⠀⇒ 12480 = P

Principal = Rs. 12480

As we know,

C.I. = Amount - Principal

So,

Amount = C.I. + Principal

⠀⠀⠀⇒ Amount = 6500.52 + 12480

⠀⠀⠀⇒ Amount = 18,980.52

★ Amount = Rs. 18,980.52