Simple Interest
MCQs Math


Question:     Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.


Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $10800

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 = $10800 – $5400 = $5400

Thus, Simple Interest = $5400

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 × 5400/5400 × 10

= 540000/54000

= 10 years (using formula)

Thus, Time (T) = 10 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) = $5400

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $5400 (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 = 10% of Principal

= 10% of $5400

= 10/100 × 5400

= 10 × 5400/100

= 54000/100 = 540

Thus, simple Interest for 1 year = $540

Now,

∵ If the simple Interest is $540, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/540 years

∴ If the simple Interest is $5400, then the time = 1/540 × 5400 years

= 1 × 5400/540 years

= 5400/540 = 10 years

Thus, time (T) = 10 years Answer


Similar Questions

(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?

(2) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.

(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?

(6) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(7) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(8) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

(9) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(10) How much loan did Ashley borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7532.5 to clear it?


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