Page 200 - Start Up Mathematics_8 (Non CCE)

Example 4: Find the compound interest on ` 1,000 for 2 years at the rate of 10% per annum compounded
annually.

Solution: Here, P = ` 1,000, R = 10%, n = 2 years

Ê R ˆ n
A = P 1+ 100¯
Á
˜
Ë
Ê 10 ˆ 2 Ê 110ˆ 2
= 1,000 1+ 100¯ = 1,000 Á Ë 100¯ ˜
˜
Á
Ë
Ê 11ˆ 2
= 1,000 × Á 10¯ = 1,210
˜
Ë
Now, C.I. = A – P = ` (1,210 – 1,000) = ` 210
Example 5: The simple interest on a certain sum of money at the rate of 4% per annum for 3 years is
` 1,200. Find the compound interest on the same amount at the rate of 10% per annum for
3 years.
Solution: Let the principal (P) be ` x.

PR T¥ ¥
We know that, S.I. =
100

x ¥¥43 12x
fi 1,200 = fi = 1,200
100 100
1 200 100, ¥
fi x = = 10,000
12

\ Principal (P) = ` 10,000

Now, P = ` 10,000, R = 10%, n = 3 years

Ê R ˆ n Ê 10 ˆ 3
A = P 1+ 100¯ = ` 10,000 1+ 100¯ ˜
˜
Á
Á
Ë
Ë
Ê
1 ˆ
= ` 10,000 1+ 10¯ ˜ 3 = ` 10,000 Ê Á Ë 11ˆ ˜ 3
Á
10¯
Ë
Ê 11 11 11ˆ
= ` 10 000, ¥ 10 ¥ 10 ¥ 10¯ = ` 13,310
Á
˜
Ë
Hence, C.I. = A – P = ` (13,310 – 10,000) = ` 3,310
Example 6: Find the difference in the simple interest and the compound interest on ` 625 for 2 years at
the rate of 4% per annum.

Solution: P = ` 625, T = 2 years, R = 4% per annum
PR T¥ ¥ 625 42¥¥
\ S.I. = = = ` 50
100 100

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