Simple Interest
MCQs Math

Question:     Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution And Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $7668

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 = $7668 – $5400 = $2268

Thus, Simple Interest = $2268

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 × 2268}/_{5400 × 6}

= ²²⁶⁸⁰⁰/₃₂₄₀₀

= 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) = 6% per annum

Simple Interest = $2268 (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 $2268, then the time = ¹/₃₂₄ × 2268 years

= ^{1 × 2268}/₃₂₄ years

= ²²⁶⁸/₃₂₄ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.

(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?

(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.

(5) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.

(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.

(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.

(9) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.