 # In Simple Interest when the Time is given in Months and Days | Simple Interest Formula in Months

Most of the candidates get confused to solve simple interest problems when time is given in months and days. Here, we are providing easy ways to clear your confusion. In Simple Interest when the Time is given in Months and Days, it is easy to find Principal Amount / Interest. Recall the concept of Simple Interest in months and ways to calculate these problems. You can come across these problems in various sectors like Banking, Finance, Automobile, etc.

If you borrow money from someone or a bank, then you have to repay them with interest. Know the simple interest formulas when time is given in months and days in the below sections. Check out tips and tricks to solve Simple Interest in Months and Days Problems.

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## How to Calculate Simple Interest when given Months and Days?

To calculate the simple interest on a yearly basis, we use the formula

Simple Interest = (P * T * R) / 100

where P is the Principal Amount

T is the Duration of the time

R is the Interest Rate

The amount can be calculated using the formula

Amount(A) = Principal (P) + Interest(I)

When the time is given in months we use a special formula to calculate it. Suppose that R is the rate of interest per annum, P is the principal amount, T be the time(in months), we use the formula as

SI for n months = (P * n * R) / (12 * 100)

### Another Method to Calculate Simple Interest in Months

When the time is given in months, we have to convert it to years and then find simple interest. To convert it into years divide it by 12 and then on further simplification, consider its value.

#### How to find Simple Interest when Time is in Months?

Step 1: Determine the total amount of money borrowed

In the first step, we have to determine the total amount of money borrowed which is called the principal. The amount you invested is known as the principal amount which is represented by “P”.

Example: Suppose that Ramu bought an auto for $8000 and he paid the down payment of$2000 and the rest as financed. Then, the principal amount on the auto would be $6000 Step 2: Convert the rate of interest into the decimal value In the next step, you have to convert the rate of interest into the decimal value. The rate of interest is typically expressed in percentages. You have to divide the percentage into the decimal value. Use that value in the formula. Example: If the auto loan has a rate of interest of 5%, then we can express the simple interest value as 0.05 Step 3: Use the time period for the loan length In the next step, we determine the time period. Loans are generally made for certain years and they are represented by “T”. If the time period is given in months, then convert it to years by using the formula SI for n months = (P * n * R) / (12 * 100) Example: If Ramu took out a 36-month car loan scheme, then we have to divide 30 by 12 (thus the time will be converted into years). Therefore the loan is 3 years. Step 4: Find the total interest using the formula Once, we get the final data, then multiply them together and determine the interest amount over the investment or loan. As mentioned in the above example, Ramu financed a car with a$6000 loan at 5% interest for 3 years.

P = 6,000

r = 0.05

t = 3

Hence, the interest owned is P * R * T = 6,000 * 0.05 * 3

I = 900

Step 5: Calculate the total amount on the loan

When you have to calculate the payback loan with simple interest, then you have to add the originally borrowed money and total interest. We use the formula as I + P. As mentioned in the above example,I = 900, P = 6000Therefore, the value is 900 + 6000 = 6900If we have to calculate the total amount of money over the loan, then we use the formula A = P(1 + rt)

### Simple Interest Calculation when Time is in Days

Whenever the time is given in days, we just have to divide the time with 365 and convert it into years. We use the same steps as above to solve the problems once we convert the time into years.

### Simple Interest Calculation Examples When Time is in Months and Days

Problem 1:

Ivan is investing $4000 for 24 months. The interest rate is 5.5% How much interest will Ivan earn after 24 months? Solution: As given in the question, Principal amount (P) =$4000

Interest rate (R) = 5.5%

Time = 24 months
First Method:
To convert the time in months to years, we use the direct formula as
(P * n * R) / (12 * 100)
= (4000 * 24 * 5.5) /(12 * 100)
On further simplification, we get the final solution as
I = 440
Therefore, Interest that Ivan will earn after 12 months is $440 Second Method: First, we collect all the data and then convert the time into months As given the time is 24 months We convert into years, therefore we divide it by 12. Therefore, it is 24/12 = 2 years Now, we substitute the complete data in the equation Simple Interest = (P * T * R) / 100 SI = (4000 * 2 * 5.5) / 100 On further simplification, we get the final result as SI =$440

Problem 2:

Shiren got a $1200 loan for 36 months. She paid$90 in interest. What was the interest rate?

Solution:

As given in the question,

Principal amount (P) = $1200 Time (t) = 36 months Interest (I) = 90 First Method: To convert the months into years, we use the formula as (P * n * R) / (12 * 100) = (1200 * 36 * R ) / (12 * 100) On further simplification, we get the final result as R = 3.75% Therefore, the rate of interest = 3.75% Second Method: First, we collect all the data and then convert the time into months As given the time is 36 months We convert into years, therefore we divide it by 12. Therefore, it is 36/12 = 3 years Now, we substitute the complete data in the equation Simple Interest = (P * T * R) / 100 90 = 1200 * 3 * R / 100 On further simplification, we get the final result as R = 3.75% Therefore, the rate of interest is 3.75% Problem 3: Find the simple interest for$7800 at 3.7% ordinary interest for 65 days?

Solution:

As given in the question,

Principal (P) = $7800 Rate of Interest = 3.7% Time = 65 days To convert days into years, we have to divide it by 365 Therefore, we get time as 65/365 = 0.178 Now, substitute all the values in the equation, SI = P * T * R / 100 SI = 7800 * 0.178 * 3.7 /100 SI =$51.37

Therefore, the simple interest is \$51.37

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