Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4700

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $7238

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 = $7238 – $4700 = $2538

Thus, Simple Interest = $2538

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 × 2538}/_{4700 × 9}

= ²⁵³⁸⁰⁰/₄₂₃₀₀

= 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) = $4700

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $2538 (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 = 9% of Principal

= 9% of $4700

= ⁹/₁₀₀ × 4700

= ^{9 × 4700}/₁₀₀

= ⁴²³⁰⁰/₁₀₀ = 423

Thus, simple Interest for 1 year = $423

Now,

∵ If the simple Interest is $423, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₃ years

∴ If the simple Interest is $2538, then the time = ¹/₄₂₃ × 2538 years

= ^{1 × 2538}/₄₂₃ years

= ²⁵³⁸/₄₂₃ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(4) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?

(6) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.

(8) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?

(9) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(10) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?