Page 135 - ICSE Math 8

AT A GLANCE

Ô
Ê R ˆ n Ï Ê Ô R ˆ n ¸
˜
¾ If the interest is compounded annually, then A = P 1+ 100¯ and C.I. = A – P = P Á Ì Ë 1+ 100¯ - 1 ˝ .
Á
˜
Ë
Ó Ô
˛ Ô
¾ If the interest is compounded m times in a year, then
Ô
Ê R ˆ mn Ï Ê Ô R ˆ mn ¸
A = P 1+ 100 ¯ ˜ and C.I. = A – P = Ì Á 1+ 100 ¯ ˜ - 1 ˝
Á
Ë
Ë
m
m
Ó Ô
˛ Ô
¾ If different years have different rates of interest, then
Ê R ˆ Ê R ˆ Ê R ˆ Ê R ˆ
n
3
2
1
A = P 1+ 100¯ Ë 1+ 100¯ Ë 1+ 100¯ ˜ ... 1+ 100¯ and C.I. = A – P
˜ Á
˜ Á
˜
Á
Á
Ë
Ë
l
¾ If the interest is compounded annually but the time is in fraction of a year, i.e., n where
Ê ˆ m
n
l Ê R ˆ Á lR ˜
Á
˜ Á
Ë
m Æ fra ction of a year, then A = P 1+ 100¯ 1+ m ˜ and C.I. = A – P
Á 100˜
Ë ¯
¾ If P Æ asset value, R% Æ rate of appreciation/depreciation, n Æ number of years and R %, R %, ...,
1
2
R % Æ rate of appreciation/depreciation for 1st, 2nd, ..., nth year then,
n
R
ˆ
Ê
(a) appreciated asset value after n years = P 1+ 100¯ n
˜
Á
Ë
Ê R ˆ Ê R ˆ Ê R n ˆ
2
1
(b) appreciated asset value after n years = P 1+ 100¯ Ë 1+ 100¯ ˜ ... 1+ 100¯
˜ Á
˜
Á
Á
Ë
Ë
Ê R ˆ n
(c) depreciated asset value after n years = P 1- 100¯
˜
Á
Ë
Ê R ˆ Ê R ˆ Ê R ˆ
2
n
1
(d) depreciated asset value after n years = P 1- 100¯ Ë 1- 100¯ ˜ ... 1- 100¯
˜ Á
˜
Á
Á
Ë
Ë
MENTAL MATHS
1. Choose the correct option.
(a) The amount on ` 1,000 for 2 years at the rate of 5% per annum is:
(i) ` 1,100 (ii) ` 1,102.50 (iii) ` 1,102.25 (iv) ` 1,100.50
(b) The compound interest on ` 20,000 for 2 years at the rate of 10% per annum is:
(i) 4,000 (ii) 2,050 (iii) 4,200 (iv) 4,310
(c) If the interest is compounded half-yearly, then to find the amount, we __________ the given time.
(i) half (ii) double (iii) triple (iv) make no change
(d) Compound interest is:
(i) always less than simple interest (ii) always equal to simple interest
(iii) always greater than simple interest (iv) always greater than or equal to simple interest
(e) The difference between the compound interest and simple interest on ` 500 at the rate of 10% per
annum for 1 year is:
(i) 0 (ii) ` 20 (iii) ` 10 (iv) ` 50
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