Simple Interest
MCQs Math


Question:     Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.


Correct Answer  8

Solution And Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $7740

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 = $7740 – $4500 = $3240

Thus, Simple Interest = $3240

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 × 3240/4500 × 9

= 324000/40500

= 8 years (using formula)

Thus, Time (T) = 8 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) = $4500

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

Simple Interest = $3240 (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 $4500

= 9/100 × 4500

= 9 × 4500/100

= 40500/100 = 405

Thus, simple Interest for 1 year = $405

Now,

∵ If the simple Interest is $405, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/405 years

∴ If the simple Interest is $3240, then the time = 1/405 × 3240 years

= 1 × 3240/405 years

= 3240/405 = 8 years

Thus, time (T) = 8 years Answer


Similar Questions

(1) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.

(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.

(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 7% simple interest?

(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?

(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?

(7) If Kimberly paid $5208 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(9) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.

(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.


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