Simple Interest
MCQs Math


Question:     Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.


Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $10260

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 = $10260 – $5400 = $4860

Thus, Simple Interest = $4860

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 × 4860/5400 × 9

= 486000/48600

= 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) = $5400

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

Simple Interest = $4860 (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 $5400

= 9/100 × 5400

= 9 × 5400/100

= 48600/100 = 486

Thus, simple Interest for 1 year = $486

Now,

∵ If the simple Interest is $486, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/486 years

∴ If the simple Interest is $4860, then the time = 1/486 × 4860 years

= 1 × 4860/486 years

= 4860/486 = 10 years

Thus, time (T) = 10 years Answer


Similar Questions

(1) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?

(2) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(3) 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.

(4) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(5) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.

(7) If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?

(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?


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