Simple Interest
Math MCQs

Question :    Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $6407

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 = $6407 – $4300 = $2107

Thus, Simple Interest = $2107

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 × 2107}/_{4300 × 7}

= ²¹⁰⁷⁰⁰/₃₀₁₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4300

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

Simple Interest = $2107 (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 $4300

= ⁷/₁₀₀ × 4300

= ^{7 × 4300}/₁₀₀

= ³⁰¹⁰⁰/₁₀₀ = 301

Thus, simple Interest for 1 year = $301

Now,

∵ If the simple Interest is $301, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₁ years

∴ If the simple Interest is $2107, then the time = ¹/₃₀₁ × 2107 years

= ^{1 × 2107}/₃₀₁ years

= ²¹⁰⁷/₃₀₁ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.

(2) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.

(4) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.

(7) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.

(9) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?