Simple Interest
MCQs Math


Question:     Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.


Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $11600

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 = $11600 – $5800 = $5800

Thus, Simple Interest = $5800

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 × 5800/5800 × 10

= 580000/58000

= 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) = $5800

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

Simple Interest = $5800 (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 $5800

= 10/100 × 5800

= 10 × 5800/100

= 58000/100 = 580

Thus, simple Interest for 1 year = $580

Now,

∵ If the simple Interest is $580, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/580 years

∴ If the simple Interest is $5800, then the time = 1/580 × 5800 years

= 1 × 5800/580 years

= 5800/580 = 10 years

Thus, time (T) = 10 years Answer


Similar Questions

(1) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?

(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.

(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?

(5) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(8) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.

(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.


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