Simple Interest
Math MCQs

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 & 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 after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

(2) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?

(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.

(4) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?

(5) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

(7) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.

(9) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(10) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?