Simple Interest
MCQs Math


Question:     Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.


Correct Answer  7

Solution And Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $8493

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 = $8493 – $5700 = $2793

Thus, Simple Interest = $2793

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 × 2793/5700 × 7

= 279300/39900

= 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) = $5700

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

Simple Interest = $2793 (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 $5700

= 7/100 × 5700

= 7 × 5700/100

= 39900/100 = 399

Thus, simple Interest for 1 year = $399

Now,

∵ If the simple Interest is $399, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/399 years

∴ If the simple Interest is $2793, then the time = 1/399 × 2793 years

= 1 × 2793/399 years

= 2793/399 = 7 years

Thus, time (T) = 7 years Answer


Similar Questions

(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.

(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.

(4) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?

(5) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.

(6) If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.

(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.

(10) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?


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