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

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    Compound Interest by Using Formula, when it is calculated annuallyWhen the interest is compounded annuallyA = P (1 + R/100)ⁿ1. Find the amount of $ 8000 for 3 years, compounded annually 5% per annum. Also, find the compound interest. 2. Find the compound interest on $ 6400 for 2 years, compounded annually 7¹/₂ % per annum. When the interest is compounded annually but rates are different for different years1. Find the amount of $ 12000 after 2 years, compounded annually; the rate of interest being 5 % p..a. during the first year and 6 % p..a. during the second year. Also, find the compound interest. When interest is compounded annually but time is a fraction1. Find the compound interest on $ 31250 8 % per annum for 2 years. Solution Amount after 2³/₄ years Compound Interest by
    Using Formula, when it is calculated half-yearlyInterest Compounded Half-Yearly1. Find the compound interest on $ 15625 for 1¹/₂
    years 8 % per annum when compounded half-yearly. 2. Find the compound interest on $ 160000 for 2 years 10% per annum when compounded semi-annually. Compound Interest by Using Formula, when it is calculated QuarterlyInterest Compounded
    Quarterly1. Find the compound interest on $ 125000, if Mike took loan from a bank for 9 months 8 % per annum, compounded quarterly. What is the compound interest on PHP 6500 for 2 years compounded an interest being 5% per annum during the first year and 6% per annum during second year?What is the compound interest on Rs 6500 for 2 years rate of interest 4% per annum?What is the compound interest on Rs 3000 6% pa for 2 years?What is the compound interest on 15000 for 2 years?

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

Compound Interest by Using Formula, when it is calculated annually

Case I:

When the interest is compounded annually

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 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.

2. Find the compound interest on $ 6400 for 2 years, compounded annually 7¹/₂ % per annum.

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:

When the interest is compounded annually but rates are different for different years

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.

1. Find the amount of $ 12000 after 2 years, compounded annually; the rate of interest being 5 % p..a. during the first year and 6 % p..a. during the second year. Also, find the compound interest.

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:

When interest is compounded annually but time is a fraction

For example suppose time is 2³/₅ years then,

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

1. Find the compound interest on $ 31250 8 % per annum for 2 years. Solution Amount after 2³/₄ years

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.

Compound Interest by
Using Formula, when it is calculated half-yearly

Interest Compounded Half-Yearly

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).

1. Find the compound interest on $ 15625 for 1¹/₂
years 8 % per annum when compounded half-yearly.

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.

2. Find the compound interest on $ 160000 for 2 years 10% per annum when compounded semi-annually.

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.

Compound Interest by Using Formula, when it is calculated Quarterly

Interest Compounded
Quarterly

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).

1. Find the compound interest on $ 125000, if Mike took loan from a bank for 9 months 8 % per annum, compounded quarterly.

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

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

Problems on Compound Interest

Variable Rate of Compound Interest

Difference of Compound Interest and Simple Interest

Practice Test on Compound Interest

Uniform Rate of Growth

Uniform Rate of Depreciation

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

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What is the compound interest on PHP 6500 for 2 years compounded an interest being 5% per annum during the first year and 6% per annum during second year?

Hence, we can say that Rs. 734.5 is the compound interest on Rs. 6500 for 2 years.

What is the compound interest on Rs 6500 for 2 years rate of interest 4% per annum?

Hence, the interest earned is Rs 734.5.

What is the compound interest on Rs 3000 6% pa for 2 years?

Detailed Solution
∴ The compound interest for 2 years is Rs. 1320.

What is the compound interest on 15000 for 2 years?

A = ₹ 18,816. Q.. Calculate the amount on ₹ 15,000 in 2 years 12 % compounded annually.
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