calculate interest and amount when [principal is 250] (rate of interest =7%][ and time is 4 yrs ] please answer tomorrow i have exam
Answers
Answer:
Step-by-step explanation:
Principal: The money which we deposit in or the lower from the bank or the money learned called the principal.
Rate of interest: The interest paid on $ 100 for one year is called the rate per cent per year or rate per cent per annum.
Time: The period of time for which the money is lent or invested.
Interest: Additional money paid by the borrowed to the lender for using the money is called interest.
Simple Interest: If the interest is calculated uniformly on the original principal throughout the lone period, it is called simple interest.
Amount: The total money paid back to the lender is called the amount.
Calculate Simple Interest
Formula to calculate Simple Interest?
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
Answer:
P = 250
R =7%
T = 4 years
SI = PRT/100
= 250 × 7 × 4/100
= 70
Amount = P + I
= 250 + 70
= 320