Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5000

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

Amount (A) = $8000

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 = $8000 – $5000 = $3000

Thus, Simple Interest = $3000

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 × 3000}/_{5000 × 10}

= ³⁰⁰⁰⁰⁰/₅₀₀₀₀

= 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) = $5000

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

Simple Interest = $3000 (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 $5000

= ¹⁰/₁₀₀ × 5000

= ^{10 × 5000}/₁₀₀

= ⁵⁰⁰⁰⁰/₁₀₀ = 500

Thus, simple Interest for 1 year = $500

Now,

∵ If the simple Interest is $500, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₀₀ years

∴ If the simple Interest is $3000, then the time = ¹/₅₀₀ × 3000 years

= ^{1 × 3000}/₅₀₀ years

= ³⁰⁰⁰/₅₀₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?

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

(3) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.

(5) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?

(6) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?

(7) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

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

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