It is very easy to calculate compound interest by using formula.

We can derive general formulae for calculating compound interest in various cases, as given below.

**Case I:**

Let principal = $ P, rate = R % per annum and time = n years.

Then, the amount A is given by the formula

A = P (1 + R/100)ⁿ

1. Find the amount of $ 8000 for 3 years, compounded annually at 5% per annum. Also, find the compound interest.

**Solution:**

Here, P = $ 8000, R = 5 % per annum and n = 3 years.

Using the formula A = $ P(1 + R/ 100)ⁿ

amount after 3 years = $ {8000 × (1 + 5/100)³}

= $ (8000 × 21/20 × 21/20 × 21/20)

= $ 9261.

Thus, amount after 3 years = $ 9261.

And, compound interest = $ (9261 - 8000)

**Therefore, compound interest = $ 1261.**

**Solution:**

Here, P = $ 6400, R % p. a. and n = 2 years.

Using the formula A = P (1 + R/100)ⁿ

Amount after 2 years = [6400 × {1 + 15/(2 × 100)}²]

= $ (6400 × 43/40 × 43/40)

=$ 7396.

Thus, amount = $ 7396

and compound interest = $ (7396 - 6400)

**Therefore, compound interest = $ 996.**

**Case 2: **

Let principal = $ P, time = 2 years, and let the rates of interest be p % p.a. during the first year and q % p.a. during the second year.

Then, amount after 2 years = $ {P × (1 + P/100) × (1 + q/100)}.

This formula may similarly be extended for any number of years.

**Solution:**

Here, P = $12000, p = 5 % p.a. and q = 6 % p.a.

Using the formula A = {P × (1 + P/100) × (1 + q/100)}

amount after 2 years = $ {12000 × (1 + 5/100) × (1 + 6/100)}

= $ (12000 × 21/20 × 53/50)

=$ 13356

Thus, amount after 2 years = $ 13356

And, compound interest = $ (13356 – 12000)

**Therefore, compound interest = $ 1356.**

**Case 3: **

For example suppose time is 2³/₅ years then,

Amount = P × (1 + R/100)² × [1 + (3/5 × R)/100]

**Solution:**

Amount after 2³/₄ years

= $ [31250 × (1 + 8/100)² × (1 + (3/4 × 8)/100)]

= ${31250 × (27/25)² × (53/50)}

= $ (31250 × 27/25 × 27/25 × 53/50)

= $ 38637.

Therefore, Amount = $ 38637,

Hence, compound interest = $ (38637 - 31250) = $ 7387.

Let principal = $ P, rate = R% per annum, time = a years.

Suppose that the interest is compounded half- yearly.

Then, rate = (R/2) % per half-year, time = (2n) half-years, and

amount = P × (1 + R/(2 × 100))²ⁿ

Compound interest = (amount) - (principal).

**Solution:**

Here, principal = $ 15625, rate = 8 % per annum = 4% per half-year,

time = 1¹/₂ years = 3 half-years.

Amount = $ [15625 × (1 + 4/100)³]

=$ (15625 × 26/25 × 26/25 × 26/25)= $ 17576.

Compound interest = $ (17576 - 15625) = $ 1951.

**Solution:**

Here, principal = $ 160000, rate = 10 % per annum = 5% per half-year, time = 2 years = 4 half-years.

Amount = $ {160000 × (1 + 5/100)⁴}

=$ (160000 × 21/20 × 21/20 × 21/20 × 21/20)

compound interest = $ (194481- 160000) = $ 34481.

Let principal = $ P. rate = R % per annum, time = n years.

Suppose that the interest is compounded quarterly.

Then, rate = (R/4) % Per quarter, time = (4n) quarters, and

amount = P × (1 + R/(4 × 100))⁴ⁿ

Compound interest = (amount) - (principal).

**Solution:**

Here, principal = $ 125000,

rate = 8 % per annum = (8/4) % per quarter = 2 % per quarter,

time = 9 months = 3 quarters.

Therefore, amount = $ {125000 × ( 1 + 2/100)³}

=$ (125000 × 51/50 × 51/50 × 51/50)= $ 132651

Therefore, compound interest $ (132651 - 125000) = $ 7651.

**● Compound Interest**

**Compound Interest with Growing Principal**

**Compound Interest with Periodic Deductions**

**Compound Interest by Using Formula**

**Compound Interest when Interest is Compounded Yearly**

**Compound Interest when Interest is Compounded Half-Yearly**

**Compound Interest when Interest is Compounded Quarterly**

**Variable Rate of Compound Interest**

**Difference of Compound Interest and Simple Interest**

**Practice Test on Compound Interest**

**Uniform Rate of Growth and Depreciation**

**● Compound Interest - Worksheet**

**Worksheet on Compound Interest**

**Worksheet on Compound Interest when Interest is Compounded Half-Yearly**

**Worksheet on Compound Interest with Growing Principal**

**Worksheet on Compound Interest with Periodic Deductions**

**Worksheet on Variable Rate of Compound Interest**

**Worksheet on Difference of Compound Interest and Simple Interest**

**Worksheet on Uniform Rate of Growth**

**Worksheet on Uniform Rate of Depreciation**

**Worksheet on Uniform Rate of Growth and Depreciation**

**8th Grade Math Practice** **From Compound Interest by Using Formula to HOME PAGE**

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