Simple Interest
MCQs Math


Question:     Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.


Correct Answer  7

Solution And Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $9798

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 = $9798 – $6900 = $2898

Thus, Simple Interest = $2898

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 × 2898/6900 × 6

= 289800/41400

= 7 years (using formula)

Thus, Time (T) = 7 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) = $6900

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

Simple Interest = $2898 (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 $6900

= 6/100 × 6900

= 6 × 6900/100

= 41400/100 = 414

Thus, simple Interest for 1 year = $414

Now,

∵ If the simple Interest is $414, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/414 years

∴ If the simple Interest is $2898, then the time = 1/414 × 2898 years

= 1 × 2898/414 years

= 2898/414 = 7 years

Thus, time (T) = 7 years Answer


Similar Questions

(1) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.

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

(4) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.

(7) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?

(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.

(10) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?


NCERT Solution and CBSE Notes for class twelve, eleventh, tenth, ninth, seventh, sixth, fifth, fourth and General Math for competitive Exams. ©