Page 205 - Start Up Mathematics_8 (Non CCE)

¸
Ï
10 ˆ
Ô
R
Ê
A = P 1+ 100¯ ˆ ˜ n fi 378 = 1,800 Ì Ê Ô Á Ë 1+ 100¯ ˜ n - 1 ˝
Á
Ë
˛ Ô
Ó Ô
Ê 10 ˆ n 378 Ê 10 ˆ n
fi 2,178 = 1,800 1+ 100¯ fi 1 800, = 1+ 100¯ - 1
˜
Á
Á
˜
Ë
Ë
2 178, Ê 1 ˆ n Ê 1 ˆ n 378
fi = 1+ ˜ fi 1+ ˜ = 1 +
Á
Á
1 800, Ë 10¯ Ë 10¯ 1 800,
Ê 11ˆ n 2 178, 121 = 1 800 378, + = 2 178,
fi Á Ë 10¯ ˜ = 1 800, = 100 1 800, 1 800,
Ê 11ˆ n = 121 = Ê 11ˆ 2

fi
˜
Ë
Ê 11ˆ n Ê 11ˆ 2 Á Ë 10¯ ˜ 100 Á 10¯
fi Á Ë 10¯ ˜ = Á Ë 10¯ ˜ n 2
11ˆ
fi n = 2 fi Ê Á Ë 11ˆ ˜ = Ê Á Ë 10¯ ˜ fi n = 2
10¯
( If the bases are equal then powers ( If the bases are equal then powers are

are equal.) equal.)
Hence, the required time is 2 years. Hence, the required time is 2 years.

Computing the interest rate percent per annum
Example 15: At what rate percent will a sum of ` 1,000 amount to ` 1,102.50 in 2 years when the interest
is compounded annually?
Solution: P = ` 1,000, A = ` 1,102.50, n = 2 years
Let the rate% be R.

Ê R ˆ n Ê R ˆ 2
A = P 1+ 100¯ ˜ fi 1,102.50 = 1,000 1+ 100¯ ˜
Á
Á
Ë
Ë
1102 5, . Ê R ˆ 2 441 Ê R ˆ 2
fi = Á 1+ ˜ fi = Á 1+ ˜
1 000, Ë 100 ¯ 400 Ë 100 ¯

Ê R ˆ 2 Ê 21ˆ 2 R 21
fi 1+ 100¯ ˜ = Á Ë 20¯ fi 1 + 100 = 20
˜
Á
Ë
R 21 21 20-
fi = – 1 =
100 20 20

R 1 100
fi = fi R = = 5
100 20 20

Hence, rate is 5% per annum.
Example 16: Harshita borrowed a certain sum of money from Seema for 2 years at simple interest. Harshita
then lent this sum to Alka at the same rate for 2 years at compound interest. At the end of
2 years, she received ` 120 as compound interest but paid ` 100 as simple interest. Find the
sum and rate of interest.

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