Simple Interest
MCQs Math


Question:     Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.


Correct Answer  7

Solution And Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8520

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 = $8520 – $6000 = $2520

Thus, Simple Interest = $2520

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 × 2520/6000 × 6

= 252000/36000

= 7 years (using formula)

Thus, Time (T) = 7 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) = $6000

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2520 (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 = 6% of Principal

= 6% of $6000

= 6/100 × 6000

= 6 × 6000/100

= 36000/100 = 360

Thus, simple Interest for 1 year = $360

Now,

∵ If the simple Interest is $360, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/360 years

∴ If the simple Interest is $2520, then the time = 1/360 × 2520 years

= 1 × 2520/360 years

= 2520/360 = 7 years

Thus, time (T) = 7 years Answer


Similar Questions

(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(2) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.

(3) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.

(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.

(6) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 8% simple interest?

(9) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(10) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.


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