Simple Interest
MCQs Math


Question:     Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.


Correct Answer  9

Solution And Explanation

Solution

Given,

Principal (P) = $4700

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7661

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 = $7661 – $4700 = $2961

Thus, Simple Interest = $2961

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 × 2961/4700 × 7

= 296100/32900

= 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) = $4700

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2961 (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 = 7% of Principal

= 7% of $4700

= 7/100 × 4700

= 7 × 4700/100

= 32900/100 = 329

Thus, simple Interest for 1 year = $329

Now,

∵ If the simple Interest is $329, then the time = 1 year

∴ If the simple Interest is $1, then the time = 1/329 years

∴ If the simple Interest is $2961, then the time = 1/329 × 2961 years

= 1 × 2961/329 years

= 2961/329 = 9 years

Thus, time (T) = 9 years Answer


Similar Questions

(1) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.

(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.

(4) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?

(5) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?

(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.

(9) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.


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