Simple Interest
Math MCQs

Question :    How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?

Correct Answer  $6900

Solution & Explanation

Solution

Given,

Amount (A) = $7935

Rate of Simple Interest (R) = 3%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$7935 = P (1 + 3% × 5)

⇒ $7935 = P (1 + ³/₁₀₀ × 5)

⇒ $7935 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7935 = P (1 + ¹⁵/₁₀₀)

⇒ $7935 = P (^{100 + 15}/₁₀₀)

⇒ $7935 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7935

⇒ P = ⁷⁹³⁵/_¹¹⁵/100

⇒ P = 7935 × ¹⁰⁰/₁₁₅

⇒ P = ^{7935 × 100}/₁₁₅

⇒ P = ⁷⁹³⁵⁰⁰/₁₁₅

⇒ P = $6900

Thus, the sum borrowed (P) = $6900 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 7935, then the Principal = ¹⁰⁰/₁₁₅ × 7935

= ^{100 × 7935}/₁₁₅

= ⁷⁹³⁵⁰⁰/₁₁₅

= 6900

Thus, Principal = $6900

Thus, the sum borrowed = $6900 Answer

Similar Questions

(1) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(3) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?

(5) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?

(7) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?

(9) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?