Page 212 - Start Up Mathematics_8 (Non CCE)

l
(d) if the interest is compounded annually but the time is in fraction of a year, i.e., n where
l Æ fra ction of a year, m
m
Ê ˆ
n
Ê R ˆ Á R l ˜
A = P 1+ 100¯ ˜ Á Á 1+ 100˜ ˜ and C.I. = A – P
m
Á
Ë
¯
Ë
2. 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
Ê R ˆ n
(a) asset value after n years = P 1+ 100¯
˜
Á
Ë
Ê R ˆ Ê R ˆ Ê R ˆ
n
2
1
(b) 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
Review Exercises
Multiple ChoiCe Questions
1. The amount on ` 1,000 for 2 years at the rate of 5% per annum is:
(a) ` 1,100 (b) ` 1,102.50 (c) ` 1,102.25 (d) ` 1,100.50
2. The compound interest on ` 20,000 for 2 years at the rate of 10% per annum is:
(a) 4,000 (b) 2,050 (c) 4,200 (d) 4,310
3. If the interest is compounded half-yearly, then to find the amount, we __________ the given time.
(a) half (b) double (c) triple (d) make no change
4. Compound interest is:
(a) always less than simple interest (b) always equal to simple interest
(c) always greater than simple interest (d) always greater than or equal to simple interest
5. The difference between the compound interest and simple interest on ` 500 at the rate of 10% per annum
for 1 year is:
(a) 0 (b) ` 20 (c) ` 10 (d) ` 50

solve Mentally

Fill in the Blanks

1. ____________ of interest allows a principal amount to grow at a faster rate than ____________ interest.
2. The ____________ increase in value of any asset is called appreciation.
3. The value of any asset reduces over a period of time due to ____________ and ____________ and tear.
4. The principal on which the C.I. amounts to ` 150 in 2 years at the rate of 5% per annum is equal to
____________.

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