Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8640

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 = $8640 – $5400 = $3240

Thus, Simple Interest = $3240

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 × 3240}/_{5400 × 6}

= ³²⁴⁰⁰⁰/₃₂₄₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $5400

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3240 (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 = 6% of Principal

= 6% of $5400

= ⁶/₁₀₀ × 5400

= ^{6 × 5400}/₁₀₀

= ³²⁴⁰⁰/₁₀₀ = 324

Thus, simple Interest for 1 year = $324

Now,

∵ If the simple Interest is $324, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₄ years

∴ If the simple Interest is $3240, then the time = ¹/₃₂₄ × 3240 years

= ^{1 × 3240}/₃₂₄ years

= ³²⁴⁰/₃₂₄ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?

(2) 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.

(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(5) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.

(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.

(8) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.

(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.