?
Time and distance
Relationship between speed, distance and time
Speed = Distance / Time or
Distance = Speed × Time
Average Speed = 2xy / x+y
where x km/hr is a speed for certain distance and y km/hr is a speed at for same distance covered.
- As we know, Speed = Distance/ Time. Now, if in questions Distance is constant then speed will be inversely proportional to time i.e. if speed increases ,time taken will decrease and vice versa.
Example 1 : A man covers a distance of 600m in 2min 30sec. What will be the speed in km/hr?
Speed =Distance / Time
Distance covered = 600m, Time taken = 2min 30sec = 150sec
Therefore, Speed= 600 / 150 = 4 m/sec
4m/sec = (4*18/5) km/hr = 14.4 km/ hr.
Example 2: A boy travelling from his home to school at 25 km/hr and came back at 4 km/hr. If whole journey took 5 hours 48 min. Find the distance of home and school.
In this question, distance for both speed is constant.
Average speed = (2xy/ x+y) km/hr, where x and y are speeds
Average speed = (2×25×4)/ 25+4 =200/29 km/hr
Time = 5hours 48min= 29/5 hours
Now, Distance travelled = Average speed × Time
Distance Travelled = (200/29)×(29/5) = 40 km
Therefore distance of school from home = 40/2 = 20km.
Simple and compound interest
Simple interest is calculated on the principal, or original, amount of a loan.
Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as “interest on interest.”
Simple Interest = Principal x Interest Rate x Term of the loan
= P x i x n
Compound Interest = Total amount of Principal and Interest in future (or Future Value) less the Principal amount at present called Present Value (PV). PV is the current worth of a future sum of money or stream of cash flows given a specified rate of return.
= [P (1 + i)n] – P
= P [(1 + i)n – 1]
where P = Principal, i = annual interest rate in percentage terms, and
n= number of compounding periods for a year.
Compounding Periods
When calculating compound interest, the number of compounding periods makes a significant difference. Generally, the higher the number of compounding periods, the greater the amount of compound interest. So for every $100 of a loan over a certain period, the amount of interest accrued at 10% annually will be lower than interest accrued at 5% semi-annually, which will, in turn, be lower than interest accrued at 2.5% quarterly.
In the formula for calculating compound interest, the variables “i” and “n” have to be adjusted if the number of compounding periods is more than once a year.
That is, within the parentheses, “i” or interest rate has to be divided by “n,” the number of compounding periods per year. Outside of the parentheses, “n” has to be multiplied by “t,” the total length of the investment.
Therefore, for a 10-year loan at 10%, where interest is compounded semi-annually (number of compounding periods = 2), i = 5% (i.e. 10% / 2) and n = 20 (i.e.10 x 2).