# 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.

## Alex lent Alice $300. Alice paid Alex with an interest of$15. If the rate of interest was 15%, after how many months did Alice pay Alex?

##### 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.

## An organization loaned $14,000 from a bank at 9% interest. They will pay a total of$20,300within the agreed date of payment. How long will the organization need to pay the amount?

##### 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.

## Steve withdrew $3,220 from a bank after he invested his money at 7.5% interest. If he receives an interest of$420, for how long the investmentwas made?

##### 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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