Simple Interest
Math MCQs

Question :    Joshua had to pay $5635 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5635

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$5635 = P (1 + 5% × 3)

⇒ $5635 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5635 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5635 = P (1 + ¹⁵/₁₀₀)

⇒ $5635 = P (^{100 + 15}/₁₀₀)

⇒ $5635 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5635

⇒ P = ⁵⁶³⁵/_¹¹⁵/100

⇒ P = 5635 × ¹⁰⁰/₁₁₅

⇒ P = ^{5635 × 100}/₁₁₅

⇒ P = ⁵⁶³⁵⁰⁰/₁₁₅

⇒ P = $4900

Thus, the sum borrowed (P) = $4900 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 5635, then the Principal = ¹⁰⁰/₁₁₅ × 5635

= ^{100 × 5635}/₁₁₅

= ⁵⁶³⁵⁰⁰/₁₁₅

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?

(3) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?

(5) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.

(7) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.

(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.