Question

6. If the simple interest on a sum of money for 3 years at 8% per annum is 7500, find the
compound interest on the same sum, for the same period at the same rate.​

Answer 1

Given:

• if the simple interest on a sum of money for 3 years at 8% per anum is 7500

To Find:

• the  compound interest on the same sum, for the same period at the same rate.

Solution:

➤  here we have been given the simple interest , the time and the rate of interest, so now, let us find the principal money with the given clues, so that we can find the compound interest on the sum of money.

${\underline{\frak{\dag \;As\; we \; know\;that\;}}}$

$\;\;\;\;\;\;\;\;\;\;\; {\dag} {\bf{\bigg[ Simple \; Interest = \dfrac{P\times T\times R}{100} \bigg]}}$

→ Where,

• p denotes principal
• T denotes time
• R denotes rate

→  Here,

• Simple Interest = 7500
• Time = 3 years
• Rate = 8%

→ Substituting we get,

$\longrightarrow \tt S.I = \frac{p\times t\times r}{100} \\ \\ \\ \longrightarrow \tt 7500 = \frac{p\times 3 \times 8 }{100} \;\\ \\ \\ \longrightarrow \tt p = \frac{7500\times 100}{3\times 8} \\ \\ \\ \longrightarrow \tt p= \frac{250000}{8} \\ \\ \\ \longrightarrow \tt p=31250$

• henceforth,the principal amount is rs.31250

➭ Now, let us find the compound interest.

→ We know,

$\;\;\;\;\;\;\;\;\;\;\; \dag {\bigg[ \bf A=P\bigg(1+\frac{r}{100}\bigg)^{n} \bigg] }$

→ Where,

• A = amount
• P = principal
• R = rate
• N = time

→ Here,

• p = 31250
• r = 8
• n = 3

→ Substituting we get,

$\longrightarrow \tt A = 31250 \bigg[1+\frac{8}{100} \bigg]^{3} \\ \\ \\ \longrightarrow \tt A = 31250\bigg[ \frac{108}{100} \bigg]^{3} \\ \\ \\ \longrightarrow \tt A= 31250\times \frac{108}{100} \times \frac{108}{100} \times \frac{108}{100} \\ \\ \\ \longrightarrow \tt A = {\boxed{\pmb{\frak{ Rs. 39366}}}\bigstar}$

Now,

• C.I = Amount - Principal
• C.I = 39366 - 31250
• C.I = Rs. 8116

Hence:

• the compound interest = Rupees.8116

Answer 2

Given :

• Interest (I) = Rs 7500
• Rate (R) = 8% p.a
• Time (T) = 3 years

To Find :

• The compound interest on the same sum, for the same period at the same rate.

Formulas :

• A = P [1 + R / 100]^n
• CI = A - P
• SI = P × R × T / 100

where ,

• P denotes Principal
• R denotes Rate
• n denotes Time
• T denotes Time
• A denotes Amount
• CI denotes Compound Interest
• SI denotes Simple Interest

Solution :

✰ In this question, Interest and Rate along with the Time are given and we have to find the compound interest on the same sum, for the same period at the same rate. So firstly we will [ I = P × R × T/100 ] to find the principal and then we will find the amount using [ A = P [1 + R / 100]^n ] after that we will find the compound interest using [ CI = A - P ] .

⠀⠀⠀

⟹ Interest = P × R × T / 100

⟹ Principal = I × 100/R × T

⟹ Principal = 7500 × 100/8 × 3

⟹ Principal = 750000/24

⟹ Principal = 375000/12

⟹ Principal = 187500/6

⟹ Principal = Rs 31250

⠀

Now,

⟼ Amount = P [1 + R / 100]^n

⟼ A = 31250 [1 + 8/100]³

⟼ A = 31250 [108/100]³

⟼ A = 31250 [54/50]³

⟼ A = 31250 [27/25]³

⟼ A = 31250 × 27/25 × 27/25 × 27/25

⟼ A = 31250 × 729/625 × 27/25

⟼ A = 31250 × 19683/15625

⟼ A = 2 × 19683

⟼ A = Rs 39366

⠀⠀

And,

⟼ CI = Amount - Principal

⟼ CI = 39466 - 31250

⟼ Compound Interest = Rs 8,116

⠀⠀⠀

Thus Compound Interest is Rs 8116

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