Simple Interest
MCQs Math


Question:     Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.


Correct Answer  8

Solution And Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $11696

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 = $11696 – $6800 = $4896

Thus, Simple Interest = $4896

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 × 4896/6800 × 9

= 489600/61200

= 8 years (using formula)

Thus, Time (T) = 8 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) = $6800

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4896 (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 = 9% of Principal

= 9% of $6800

= 9/100 × 6800

= 9 × 6800/100

= 61200/100 = 612

Thus, simple Interest for 1 year = $612

Now,

∵ If the simple Interest is $612, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/612 years

∴ If the simple Interest is $4896, then the time = 1/612 × 4896 years

= 1 × 4896/612 years

= 4896/612 = 8 years

Thus, time (T) = 8 years Answer


Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.

(3) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.

(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?

(6) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.

(7) If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.

(10) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?


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