Simple Interest
MCQs Math


Question:     Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.


Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $4500

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9000

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 = $9000 – $4500 = $4500

Thus, Simple Interest = $4500

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 × 4500/4500 × 10

= 450000/45000

= 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) = $4500

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4500 (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 = 10% of Principal

= 10% of $4500

= 10/100 × 4500

= 10 × 4500/100

= 45000/100 = 450

Thus, simple Interest for 1 year = $450

Now,

∵ If the simple Interest is $450, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/450 years

∴ If the simple Interest is $4500, then the time = 1/450 × 4500 years

= 1 × 4500/450 years

= 4500/450 = 10 years

Thus, time (T) = 10 years Answer


Similar Questions

(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 4 years.

(3) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.

(5) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.

(8) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?

(9) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.


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