Simple Interest
MCQs Math


Question:     William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.


Correct Answer  6

Solution And Explanation

Solution

Given,

Principal (P) = $5000

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

Amount (A) = $7100

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 = $7100 – $5000 = $2100

Thus, Simple Interest = $2100

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 × 2100/5000 × 7

= 210000/35000

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5000

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

Simple Interest = $2100 (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 $5000

= 7/100 × 5000

= 7 × 5000/100

= 35000/100 = 350

Thus, simple Interest for 1 year = $350

Now,

∵ If the simple Interest is $350, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/350 years

∴ If the simple Interest is $2100, then the time = 1/350 × 2100 years

= 1 × 2100/350 years

= 2100/350 = 6 years

Thus, time (T) = 6 years Answer


Similar Questions

(1) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.

(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(4) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.

(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?

(8) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(9) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.


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