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Simple Interest
Math MCQs


Question :    Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.


Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $12240

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 = $12240 – $6800 = $5440

Thus, Simple Interest = $5440

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 × 5440/6800 × 8

= 544000/54400

= 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) = $6800

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $5440 (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 = 8% of Principal

= 8% of $6800

= 8/100 × 6800

= 8 × 6800/100

= 54400/100 = 544

Thus, simple Interest for 1 year = $544

Now,

∵ If the simple Interest is $544, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/544 years

∴ If the simple Interest is $5440, then the time = 1/544 × 5440 years

= 1 × 5440/544 years

= 5440/544 = 10 years

Thus, time (T) = 10 years Answer


Similar Questions

(1) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(5) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.

(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 9% simple interest?

(9) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 10% simple interest?