Question

Find the compound interest on 10,000 for 12 months at 10% per annum, if the interest is compounded (a) annually 12. (b) half-yearly (c) quarterly.​

Answer 1

Answer:

Compound interest if compounds yearly = ₹1,000

Compound interest if compounds half-yearly = ₹1,025

Compound interest if compounds quarterly = ₹1,038.13

Answer 2

(a) Compounded Annually

Given

• Principal = ₹10,000.
• Time = 12months = 1year.
• Rate = 10% p.a.

To Find

• Compound Interest.

Solution

A = P(1+ R/100)^n

=> A = 10000(1+ 10/100)¹

=> A = 10000(1+ 1/10)¹

=> A = 10000 × 11/10

=> A = 11000.

C.I. = Amount - Principal

=> C.I. = 11000 - 10000

∴ Compound Interest = ₹1000.

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(b) Compounded Half-yearly

Given

• Principal = ₹10,000.
• Time = 1year = 1×2 = 2years.
• Rate = 10% = 10/2 = 5%.

To Find

• Compound Interest.

Solution

A = P(1+ R/100)^n ko

=> A = 10000(1+ 5/100)²

=> A = 10000(1+ 1/20)²

=> A = 10000 × 21/20 × 21/20

=> A = 25 × 21 × 21

=> A = ₹11,025.

C.I. = Amount - Principal

=> C.I. = 11025 - 10000

∴ Compound Interest = ₹1,025.

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(c) Compounded Quarterly

Given

• Principal = ₹10,000.
• Time = 1year = 1×4 = 4years.
• Rate = 10% = 10/4 = 2.5%.

To Find

• Compound Interest.

Solution

A = P(1+ R/100)^n

=> A = 10000(1+ 2.5/100)⁴

=> A = 10000(1+ 25/1000)⁴

=> A = 10000(1+ 1/40)⁴

=> A = 10000 × 41/40 × 41/40 × 41/40 × 41/40

=> A = ₹11038.13.

C.I. = Amount - Principal

=> C.I. = 11038.13 - 10000

∴ Compound Interest = ₹1,038.13.

Used Abbreviations

• P = Principal.
• A = Amount.
• R = Rate.
• n = Time.
• C.I. = Compound Interest.

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