Simple Interest
MCQs Math


Question:     Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.


Correct Answer  9

Solution And Explanation

Solution

Given,

Principal (P) = $4600

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

Amount (A) = $8326

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 = $8326 – $4600 = $3726

Thus, Simple Interest = $3726

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 × 3726/4600 × 9

= 372600/41400

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4600

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

Simple Interest = $3726 (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 $4600

= 9/100 × 4600

= 9 × 4600/100

= 41400/100 = 414

Thus, simple Interest for 1 year = $414

Now,

∵ If the simple Interest is $414, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/414 years

∴ If the simple Interest is $3726, then the time = 1/414 × 3726 years

= 1 × 3726/414 years

= 3726/414 = 9 years

Thus, time (T) = 9 years Answer


Similar Questions

(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.

(2) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(4) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(5) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.

(7) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?

(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?

(10) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.


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