after eight months. HUW
Find the simple interest on * 2,000 for six months at the rate of 4 -% per annum
Answers
Step-by-step explanation:
If P denotes the principal ($), R denotes the rate (percentage p.a.) and T denotes time (years), then:-
S.I = (P × R × T)/100
R = (S.I × 100)/(P × T)
P = (S.I × 100)/(R × T)
T = (S.I × 100)/(P × R)
If the denotes the amount, then A = P + S.I
Note:
● When we calculated the time period between two dates, we do not could the day on which money is deposited but we count the day on which money is retuned.
● Time is always taken according to the per cent rat.
● For converting time in days into years, divide th number of days by 365 (for ordering or lap year.)
● For converting time in month into years, divide th number of month by 12 (for ordering or lap year.)
Examples to find or calculate simple interest when principal, rate and time are known
Calculate Simple Interest
Find the simple interest on:
(a) $ 900 for 3 years 4 months at 5% per annum. Find the amount also.
Solution:
P = $ 900,
R = 5% p.a.
T = 3 years 4 months = 40/12 years = 10/3 years
Therefore, S.I = (P × R × T)/100 = (900 × 5 × 10)/(100 × 3) = $ 150
Amount = P + S.I = $ 900 + $ 150 = $ 1050
(b) $ 1000 for 6 months at 4% per annum. Find the amount also.
Solution:
P = $ 1000,
R = 4% p.a.
T = 6 months = 6/12 years
S.I = (P × R × T)/100 = (1000 × 4 × 1)/(100 × 2) = $ 20
Therefore, A = P + I = $( 1000 + 20) = $ 1020
(c) $ 5000 for 146 days at 15¹/₂% per annum.
Solution:
P = $ 5000, R = 151/2% p.a. T = 146 days
S.I = ( 5000 × 31 × 146)/(100 × 2 × 365)
= $ 10 × 31 = $ 310
(d) $ 1200 from 9ᵗʰ April to 21ˢᵗ June at 10% per annum.
Solution:
P = $ 1200, R = 10% p.a. T = 9th April to 21st June
= 73 days [April = 21, May = 31, Jun = 21, 73 days]
= 73/365 years
S.I = (1200 × 10 × 73)/(100 × 365) = $ 24
Examples to find or calculate Time when Principal, S.I and Rate are known
Calculate Simple Interest
1. In how much time dose $ 500 invested at the rate of 8% p.a. simple interest amounts to $ 580.
Solution:
Here P = $ 500, R = 8% p.a A = $ 580
Therefore S.I = A - P = $ (580 - 500) = $ 80
Therefore T = (100 × S.I)/(P × R) = (100 × 80)/(500 × 3) = 2 years
2. In how many years will a sum of $ 400 yield an interest of $ 132 at 11% per annum?
Solution:
P = $ 400, R = 11% S.I = $ 132
T = (100 × S.I)/(P × R) = (132 × 100)/(400 × 11) = 3 years
Calculate Simple Interest
3. In how many years will a sum double itself at 8 % per annum?
Solution:
Let Principal = P, then, Amount = 2P
So , S.I. = A - P = 2P – P = P
T = (100 × S.I)/(P × R) = ( 100 × P)/(P × 8) = 25/2 = 121/2 years
Calculate Simple Interest
4. In how many years will simple interest on certain sum of money at 6 1/4% Per annum be 5/8 of itself?
Solution:
Let P = $ x, then S.I = $ 5/8 x
Rate = 6 1/4% = 25/4 %
Therefore T = ( 100 × S.I)/(P × R) = ( 100 × 5/8)/(x × 25/4) x = ( 100 × 5 × x × 4)/(x × 8 × 25)
T = 10 years
Examples to find or calculate Rate per cent when Principal, S.I. and Time are known
1. Find at what rate of interest per annum will $ 600 amount to $ 708 in 3 years.
Solution:
P= $ 600 , A = $ 708 Time = 3 years
Therefore S.I. = $ 708 - $ 600 = $ Rs. 108
Now, R = ( 100 × S.I)/(P × R) = (100 × 108)/(600 × 3) = 6% p.a.
Calculate Simple Interest
2. Simple interest on a certain sum is 36/25 of the sum. Find the Rate per cent and time if they are both numerically equal.
Solution:
Let the Principal be $ X Then S.I. = 36/25 x
R = ? T = ?
Let Rate = R % per annum, then Time = R years.
So S.I. = (P × R × T)/100 → 36/25 x = (x × R × T)/100
--- ( 36 × 10 × x)/(25 × x) = R2
----- R2 = 36 × 4 ----- R = √(36 × 4) = 6 × 2
Therefore Rate = 12 % p.a. and T = 12 years
Calculate Simple Interest
3. At what rate per cent per annum will $ 6000 produce $ 300 as S.I. in 1 years?
Solution:
P= $ 600, T = 1 year S.I. = $ 300
Therefore R = ( S.I × 100)/(P × R) = ( 300 × 100)/(6000 × 1) = 5% p.a
4. At what rate per cent per annum will a sum triple itself in 12 years ?
Solution:
Let the sum be $ P, then Amount = $ 3P
S.I. = $ 3P – P = $ 2P, Time = 12 years
Now, R =( S.I × 100)/(P × R) = (100 × 2P)/(P × 12) = 50/3 = 16.6 %
Examples to find or calculate Principal when Rate, Time and S.I. are known
Calculate Simple Interest
1. What sum will yield $ 144 as S.I. in 21/2 years at 16% per annum?
Solution:
Let P = $ x, S.I. = $ 144
Time = 21/2 years or 5/2 years, Rate = 16%
So, P = ( 100 × S.I)/(P × R) = ( 100 × 144)/(16 × 5/2) = ( 100 × 144 × 2)/(16 × 5) = $ 360
2. A some amount to $ 2040 in 21/2 years at , P = ?
Solution:
Let the principal = $ x
S.I. = $ (x × 11 × 5/2 × 1/100) = $ 11x/40
Amount = P + S.I. = x/1 + 11x/40 = (40x × 11x)/40 = 51x/40
But 51x/40 = 2040
51x = 2040 × 40 ---- x = (2040 × 40)/51 = $ 1600
Calculate Simple Interest
3. A certain sum amounts to $ 6500in 2 years and to $ 8750 in 5 years at S.I. Find the sum and rate per cent per annum.
Solution:
S.I. for 3 years = Amount after 5 years – Amount after 2 years
= $ 8750 – $ 6500 = 2250
S.I. for 1 years = Rs. 2250/3 = $ 750
Therefore S.I. for 2 years = $ 500× 2 = $ 1500
So, sum = Amount after 2 years – S.I.for 2 years
= $ 6500- 1500 = $ 5000
Now, P = Rs.5000, S.I. = $ 1500, Time = 3 years
R = ( 100 × S.I)/(P × T) = (100 × 1500)/(5000 × 2) = 15%
Therefore The sum is $ 5000 and the rate