Simple Interest
MCQs Math


Question:     Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.


Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $12400

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 = $12400 – $6200 = $6200

Thus, Simple Interest = $6200

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 × 6200/6200 × 10

= 620000/62000

= 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) = $6200

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

Simple Interest = $6200 (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 $6200

= 10/100 × 6200

= 10 × 6200/100

= 62000/100 = 620

Thus, simple Interest for 1 year = $620

Now,

∵ If the simple Interest is $620, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/620 years

∴ If the simple Interest is $6200, then the time = 1/620 × 6200 years

= 1 × 6200/620 years

= 6200/620 = 10 years

Thus, time (T) = 10 years Answer


Similar Questions

(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?

(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.

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

(5) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(6) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.

(9) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.


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