Simple Interest
MCQs Math


Question:     Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.


Correct Answer  6

Solution And Explanation

Solution

Given,

Principal (P) = $5100

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

Amount (A) = $7242

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 = $7242 – $5100 = $2142

Thus, Simple Interest = $2142

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 × 2142/5100 × 7

= 214200/35700

= 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) = $5100

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

Simple Interest = $2142 (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 $5100

= 7/100 × 5100

= 7 × 5100/100

= 35700/100 = 357

Thus, simple Interest for 1 year = $357

Now,

∵ If the simple Interest is $357, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/357 years

∴ If the simple Interest is $2142, then the time = 1/357 × 2142 years

= 1 × 2142/357 years

= 2142/357 = 6 years

Thus, time (T) = 6 years Answer


Similar Questions

(1) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(4) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?

(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.

(9) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?

(10) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.


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