Calculating the Time

Formulas used for solving the interest use years as the unit of time. It should be observed to have consistent units of time in order to avoid miscalculations. It should be noted that the rate should be in decimal form before using it to the formula.

Here are the scenarios to be considered for solving the rate of interest:

1. Principal, rate and interest are given


Steps:


1. Divide the interest by the product of the principal and rate of interest.

2. Unit of time is in years.


We know that,

`Interest=P*Rate*Time`

where P is Principal


So,

`Time= I/(P *Rate)`

where,

P is Principal

I is Interest


2. Future amount, rate and principal are given


Steps:


1. Divide the future amount by the principal.

2. Subtract 1 from the quotient.

3. Divide the difference by the rate of interest.

4. Unit of time is in years.


We know that,

`Future Amount=P*[1+Rate*Time]`

`(Future Amount)/P=1+Rate*Time`

`(Future Amount)/P-1=Rate*Time`

`Time= ( (Future Amount)/P- 1)/R`

where

P is Principal

R is Rate


3. Future amount, time and interest are given


Steps:


1. Subtract the future amount by the interest. The result is the principal.

2. Divide the interest by the product of the principal and rate of interest.

3. Unit of time is in years.


We know that,

Interest=Principal*Rate*Time

Time=Interest/(Rate*Principal)

As,

`P=Future Amount-Interest`

Hence,

`Time= I/(Rate * (Future Amount-I))`

where

I is Interest

Note: The formula for solving the time is similar with the formula for solving the rate of interest. Just interchange the terms.


Example 1:
 4
Explanation:

Principal amount is $300.

Interest is $15.

Rate of interest is 15%.

Using the formula for solving the time;

`Time =I/(P * Rate)`

where

P is Principal

I is Interest

`Time =15/(300 * 0.15)`

`Time =1/3 years`

Converting years into months;

`1/3Years* ((12 months)/(1 year) ) = 4 months`

Therefore, Alice paid Alex after 4 months.


Example 2:
 5 years
Explanation:

Principal amount is $14,000.

Future amount is $20,300.

Rate of interest is 9%.

Using the formula for solving the time;

`Time = ((Future Amount)/P - 1)/Rate`

`Time = (20,300/(14 000)- 1)/0.09`

`Time = (1.45 -1)/0.09`

`Time = 0.45/0.09`

`Time = 5 years`

Therefore, the organization will pay the amount after 5 years.


Example 3:
 2 years
Explanation:

Future amount is $3,220.

Interest is $420

The rate of interest is 7.5%.

Using the formula for solving the rate of interest;

`Time = ( Interest)/(Rate *(Future Amount-Interest))`

`Time = ( 420)/(0.075 * (3220-420))`

`Time = ( 420)/(0.075 * 2800)`

`Time = ( 420)/210`

`Time = 2 years`

Therefore, the amount was invested for 2 years.







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