Simple Interest
MCQs Math


Question:     John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.


Correct Answer  8

Solution And Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $7920

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 = $7920 – $4400 = $3520

Thus, Simple Interest = $3520

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 × 3520/4400 × 10

= 352000/44000

= 8 years (using formula)

Thus, Time (T) = 8 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) = $4400

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

Simple Interest = $3520 (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 $4400

= 10/100 × 4400

= 10 × 4400/100

= 44000/100 = 440

Thus, simple Interest for 1 year = $440

Now,

∵ If the simple Interest is $440, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/440 years

∴ If the simple Interest is $3520, then the time = 1/440 × 3520 years

= 1 × 3520/440 years

= 3520/440 = 8 years

Thus, time (T) = 8 years Answer


Similar Questions

(1) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.

(2) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?

(3) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.

(5) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.

(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.

(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?

(8) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?


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