Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $8424

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 = $8424 – $5400 = $3024

Thus, Simple Interest = $3024

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 × 3024}/_{5400 × 8}

= ³⁰²⁴⁰⁰/₄₃₂₀₀

= 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) = $5400

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3024 (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 = 8% of Principal

= 8% of $5400

= ⁸/₁₀₀ × 5400

= ^{8 × 5400}/₁₀₀

= ⁴³²⁰⁰/₁₀₀ = 432

Thus, simple Interest for 1 year = $432

Now,

∵ If the simple Interest is $432, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₂ years

∴ If the simple Interest is $3024, then the time = ¹/₄₃₂ × 3024 years

= ^{1 × 3024}/₄₃₂ years

= ³⁰²⁴/₄₃₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(2) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?

(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?

(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.

(6) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.

(9) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.

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