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
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
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