Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6600

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

Amount (A) = $9372

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 = $9372 – $6600 = $2772

Thus, Simple Interest = $2772

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 × 2772}/_{6600 × 7}

= ²⁷⁷²⁰⁰/₄₆₂₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $6600

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

Simple Interest = $2772 (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 $6600

= ⁷/₁₀₀ × 6600

= ^{7 × 6600}/₁₀₀

= ⁴⁶²⁰⁰/₁₀₀ = 462

Thus, simple Interest for 1 year = $462

Now,

∵ If the simple Interest is $462, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₂ years

∴ If the simple Interest is $2772, then the time = ¹/₄₆₂ × 2772 years

= ^{1 × 2772}/₄₆₂ years

= ²⁷⁷²/₄₆₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.

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

(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(6) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.

(8) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.

(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.