Simple Interest
MCQs Math


Question:     Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.


Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $10640

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 = $10640 – $5600 = $5040

Thus, Simple Interest = $5040

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 × 5040/5600 × 9

= 504000/50400

= 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) = $5600

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

Simple Interest = $5040 (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 $5600

= 9/100 × 5600

= 9 × 5600/100

= 50400/100 = 504

Thus, simple Interest for 1 year = $504

Now,

∵ If the simple Interest is $504, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/504 years

∴ If the simple Interest is $5040, then the time = 1/504 × 5040 years

= 1 × 5040/504 years

= 5040/504 = 10 years

Thus, time (T) = 10 years Answer


Similar Questions

(1) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(2) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(5) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(7) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.

(9) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.


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