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 $7344 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $7344

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 = $7344 – $5400 = $1944

Thus, Simple Interest = $1944

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 × 1944}/_{5400 × 6}

= ¹⁹⁴⁴⁰⁰/₃₂₄₀₀

= 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) = $5400

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

Simple Interest = $1944 (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 $1944, then the time = ¹/₃₂₄ × 1944 years

= ^{1 × 1944}/₃₂₄ years

= ¹⁹⁴⁴/₃₂₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?

(2) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.

(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.

(6) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.

(7) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.

(9) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.