Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4400

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7172

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 = $7172 – $4400 = $2772

Thus, Simple Interest = $2772

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 × 2772}/_{4400 × 7}

= ²⁷⁷²⁰⁰/₃₀₈₀₀

= 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) = $4400

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2772 (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 = 7% of Principal

= 7% of $4400

= ⁷/₁₀₀ × 4400

= ^{7 × 4400}/₁₀₀

= ³⁰⁸⁰⁰/₁₀₀ = 308

Thus, simple Interest for 1 year = $308

Now,

∵ If the simple Interest is $308, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₈ years

∴ If the simple Interest is $2772, then the time = ¹/₃₀₈ × 2772 years

= ^{1 × 2772}/₃₀₈ years

= ²⁷⁷²/₃₀₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?

(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.

(4) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 10% simple interest?

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.

(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?

(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?

(9) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.

(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.