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# Time

Introduction

Time is an entity which is used to calculate the duration i.e.(in hours, minutes and second).This is also used in terms of months and years while calculating the interest rates(simple and compound interest), and it is used in many forms to mainly calculate duration.

Time is used in each and every aspect in the world and it is usually specified using the terms such as hours, minutes and seconds, which places an important role in calculating time. Time is represented generally as

HH:MM:SS

(06:24:12)

6 hours 24 minutes 12 seconds

Where

H = hours

M = minutes

S = seconds

## Properties of Time

• There are 86400 seconds in a day

• There are about 600,000 seconds in a week

• There are more than 2.6 million seconds in a month

• There are more than 31 million seconds in a year, more than half a million minutes in a year. If you use a year of exactly 365 days, you get the "five hundred twenty-five thousand six hundred minutes" set so wonderfully to music in "Rent".

• A nanosecond is about how much time it takes light to travel a foot (actually 0.98357106 feet).

## Time Conversion

The time is classified in different quantities as

1 second = 1000 milliseconds

1 minute = 60 seconds

1 hour = 60 minutes

1 day = 24 hours

1 week = 7 days

1 month = 4 weeks

1 year = 365.25 days

The standard time conversions are widely used through out the world and these conversions are the basic conversions of time.

Relation between hours, minute and second is:

1hour = 60minutes

1minute = 60seconds

## Time in Calculating Speed, Distance and Rate

Formula: Distance = Rate x Time

Rate = $\frac{Distance}{Time}$

Time = $\frac{Distance}{Rate}$

Time = $\frac{Distance}{Speed}$

Distance = Time x Speed

Speed = $\frac{Distance}{Time}$

Acceleration= $\frac{(vf-vi)}{t}$

Where,

vf and vi are initial and final velocity

t is the time.

## Time in Calculating Interest Rates

Compound interest

Compound interest is the amount paid on the original principal and on the interest paid for that original investment.

Formula: A=P(1+r)n

Where

P = Principal amount

r = Annual rate of interest (percentage)

n = Number of years the amount is deposited(Time in years)

A =Total amount after n years.

Simple interest

Simple interest is a amount paid to the initial amount, considering rate of interest.

Formula: I=Prt

Where

I=simple interest

P=Principal amount

t=time

Relation between P,I,r,t:

Principal (P) P = $\frac{I}{rt}$

Interest rate (r) r = $\frac{I}{Pt}$

Time period (t) t = $\frac{I}{Pr}$

Note

Time plays an important role in calculating interest rates.

## Solved Problems on Time

1) When a boy started from point A and traveled 25km at the rate of 5kmph, Calculate the time?

Given data:

Distance = 25km

Rate = 5kmph

Time = $\frac{distance}{rate}$ = $\frac{25}{5}$

Time required is 5hours.

2) An amount of 2000rupees has been borrowed with 5% annual interest.calculate the compound interest for the initial amount after 3 years?

Given data

P = 2000

r = $\frac{5}{100}$ = 0.05

n = 3

A = 2000(1+0.05)3

A = 2315.25 rupees.

3) 2000 has been borrowed and the Simple interest paid to the investment is 300 with 4% per year interest rates. Calculate the time period?

Given data,

P = $2000 r = 4% = 0.04 I = 300$

time = $\frac{300}{2000}$ x 0.04

Therefore, t = 3.75 years.