Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $10281

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 = $10281 – $6900 = $3381

Thus, Simple Interest = $3381

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 × 3381}/_{6900 × 7}

= ³³⁸¹⁰⁰/₄₈₃₀₀

= 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) = $6900

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

Simple Interest = $3381 (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 $6900

= ⁷/₁₀₀ × 6900

= ^{7 × 6900}/₁₀₀

= ⁴⁸³⁰⁰/₁₀₀ = 483

Thus, simple Interest for 1 year = $483

Now,

∵ If the simple Interest is $483, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₃ years

∴ If the simple Interest is $3381, then the time = ¹/₄₈₃ × 3381 years

= ^{1 × 3381}/₄₈₃ years

= ³³⁸¹/₄₈₃ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(4) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.

(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?

(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?

(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.

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

(10) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.