Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5800

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9280

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 = $9280 – $5800 = $3480

Thus, Simple Interest = $3480

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 × 3480}/_{5800 × 10}

= ³⁴⁸⁰⁰⁰/₅₈₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5800

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3480 (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 = 10% of Principal

= 10% of $5800

= ¹⁰/₁₀₀ × 5800

= ^{10 × 5800}/₁₀₀

= ⁵⁸⁰⁰⁰/₁₀₀ = 580

Thus, simple Interest for 1 year = $580

Now,

∵ If the simple Interest is $580, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₈₀ years

∴ If the simple Interest is $3480, then the time = ¹/₅₈₀ × 3480 years

= ^{1 × 3480}/₅₈₀ years

= ³⁴⁸⁰/₅₈₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(2) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.

(5) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.

(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.

(9) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.