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 $8316 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $8316

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 = $8316 – $5400 = $2916

Thus, Simple Interest = $2916

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 × 2916}/_{5400 × 6}

= ²⁹¹⁶⁰⁰/₃₂₄₀₀

= 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) = $5400

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

Simple Interest = $2916 (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 $2916, then the time = ¹/₃₂₄ × 2916 years

= ^{1 × 2916}/₃₂₄ years

= ²⁹¹⁶/₃₂₄ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?

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

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.

(4) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.

(7) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.

(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.