Class 8 Maths Compound interest Assignemnt

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

Therefore, compound interest = (amount) - (principal).

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.

2. Find the compound interest on $ 6400 for 2 years, compounded annually at 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 at 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 at 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 at 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 at 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 Test sample paper for class 8

1. You invest Rs 5000 at 12% interest compounded annually. How much is in the account after 2 years, assuming that you make no subsequent withdrawal or deposit?

2. Find the amount and the compound interest on Rs 4000 at 10% p.a. for 2½ years.

3. A man invests Rs 5000 for three years at a certain rate of interest, compounded annually. At the end of one year it amounts to Rs 5600. Calculate(i) the rate of interest per annum,(ii) the interest accrued in the second year,(iii) the amount at the end of the third year.

4. A sum of Rs 9600 is invested for 3 years at 10% per annum at compound interest.(i) What is the sum due at the end of the first year?(ii) What is the sum due at the end of the second year?(iii) Find the compound interest earned in two years.(iv) Find the difference between the answers (ii) and (i) and find the interest on this sum for one year.(v) Hence write down the compound interest for the third year.

5. Find the difference between the S.I. and C.I. on Rs 2500 for 2 years at 4% p.a., compound interest reckoned semi-annually.

6. Find the amount and the compound interest on Rs 8000 in 2 years if the rate is 10% for the first year and 12% for the second year.

7. A man invests Rs 6500 for 3 years at 4·5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% is deducted at the end of each year. Find the amount at the end of the third year.

8. Calculate the compound interest for the second year on Rs 8000 invested for 3 years at 10% p.a.

9. Find the sum which amounts to Rs 9261 at 10% p.a. compound interest for 18 months, interest payable half-yearly.

10. On what sum will the compound interest for 2 years at 5% p.a. be Rs 246?

11. On what sum will the compound interest (reckoned yearly) for 3 years at 6¼% per annum be Rs 408·50?

12. A man invests Rs 1200 for two years at compound interest. After one year his money amounts to Rs 1275. Find the rate of compound interest. Also find the amount which the man will get after 2 years correct to the nearest paise.

13. At what rate percent per annum compound interest will Rs 2000 amount to Rs 2315·25 in 3 years?

14. If Rs 50000 amounts to Rs 73205 in 4 years, find the rate of compound interest payable yearly. In what time will Rs 15625 amount to Rs 17576 at 4% per annum compound interest? .

Answers

1. Rs 6272 2. Rs 5082; Rs 1082


3. (i) 12% (ii) Rs 672 (iii) Rs 6952·64


4. (i) Rs 10560 (ii) Rs 11616 (iii) Rs 2016


(iv) Rs 1056, Rs 105·60 (v) Rs 1161·60


5. Rs 6·08 6. Rs 9856; Rs 1856 7. Rs 7227·56


8. Rs 880 9. Rs 8000 10. Rs 2400 11. Rs 2048


12. 6¼%; Rs 1354·69 13. 5% 14. 10%


15. 3 years