Simple Interest
MCQs Math

Question:     John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $7920

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 = $7920 – $4400 = $3520

Thus, Simple Interest = $3520

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 × 3520}/_{4400 × 8}

= ³⁵²⁰⁰⁰/₃₅₂₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 8% per annum

Simple Interest = $3520 (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 $4400

= ⁸/₁₀₀ × 4400

= ^{8 × 4400}/₁₀₀

= ³⁵²⁰⁰/₁₀₀ = 352

Thus, simple Interest for 1 year = $352

Now,

∵ If the simple Interest is $352, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₂ years

∴ If the simple Interest is $3520, then the time = ¹/₃₅₂ × 3520 years

= ^{1 × 3520}/₃₅₂ years

= ³⁵²⁰/₃₅₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.

(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.

(6) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?

(7) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.

(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?

(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.