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Simple Interest
Math MCQs


Question :    James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.


Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $5440

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $5440 – $4000 = $1440

Thus, Simple Interest = $1440

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = 100 × Simple Interest/Principal × Rate of Interest

⇒ T = 100 × SI/P × R

Thus, Time (T) = 100 × 1440/4000 × 6

= 144000/24000

= 6 years (using formula)

Thus, Time (T) = 6 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $4000

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $1440 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 6% of Principal

= 6% of $4000

= 6/100 × 4000

= 6 × 4000/100

= 24000/100 = 240

Thus, simple Interest for 1 year = $240

Now,

∵ If the simple Interest is $240, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/240 years

∴ If the simple Interest is $1440, then the time = 1/240 × 1440 years

= 1 × 1440/240 years

= 1440/240 = 6 years

Thus, time (T) = 6 years Answer


Similar Questions

(1) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.

(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?

(3) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.

(5) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.

(7) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.

(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?

(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.