Simple Interest
MCQs Math


Question:     Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.


Correct Answer  7

Solution And Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $8791

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 = $8791 – $5900 = $2891

Thus, Simple Interest = $2891

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 × 2891/5900 × 7

= 289100/41300

= 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) = $5900

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2891 (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 = 7% of Principal

= 7% of $5900

= 7/100 × 5900

= 7 × 5900/100

= 41300/100 = 413

Thus, simple Interest for 1 year = $413

Now,

∵ If the simple Interest is $413, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/413 years

∴ If the simple Interest is $2891, then the time = 1/413 × 2891 years

= 1 × 2891/413 years

= 2891/413 = 7 years

Thus, time (T) = 7 years Answer


Similar Questions

(1) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

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

(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?

(4) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(7) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.

(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.


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