Simple Interest
Math MCQs

Question :    Paul had to pay $5405 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  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $5405

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

$5405 = P (1 + 5% × 3)

⇒ $5405 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5405 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5405 = P (1 + ¹⁵/₁₀₀)

⇒ $5405 = P (^{100 + 15}/₁₀₀)

⇒ $5405 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5405

⇒ P = ⁵⁴⁰⁵/_¹¹⁵/100

⇒ P = 5405 × ¹⁰⁰/₁₁₅

⇒ P = ^{5405 × 100}/₁₁₅

⇒ P = ⁵⁴⁰⁵⁰⁰/₁₁₅

⇒ P = $4700

Thus, the sum borrowed (P) = $4700 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 5405, then the Principal = ¹⁰⁰/₁₁₅ × 5405

= ^{100 × 5405}/₁₁₅

= ⁵⁴⁰⁵⁰⁰/₁₁₅

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

(2) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.

(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(5) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.

(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(7) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?

(10) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.