Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $9454

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 = $9454 – $5800 = $3654

Thus, Simple Interest = $3654

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 × 3654}/_{5800 × 7}

= ³⁶⁵⁴⁰⁰/₄₀₆₀₀

= 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) = $5800

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

Simple Interest = $3654 (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 $5800

= ⁷/₁₀₀ × 5800

= ^{7 × 5800}/₁₀₀

= ⁴⁰⁶⁰⁰/₁₀₀ = 406

Thus, simple Interest for 1 year = $406

Now,

∵ If the simple Interest is $406, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₆ years

∴ If the simple Interest is $3654, then the time = ¹/₄₀₆ × 3654 years

= ^{1 × 3654}/₄₀₆ years

= ³⁶⁵⁴/₄₀₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) If William paid $4200 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 after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.

(3) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?

(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?

(6) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.

(8) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?

(9) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.