Simple Interest
Math MCQs

Question :    John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3584

Rate of Simple Interest (R) = 4%

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

$3584 = P (1 + 4% × 3)

⇒ $3584 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3584 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3584 = P (1 + ¹²/₁₀₀)

⇒ $3584 = P (^{100 + 12}/₁₀₀)

⇒ $3584 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3584

⇒ P = ³⁵⁸⁴/_¹¹²/100

⇒ P = 3584 × ¹⁰⁰/₁₁₂

⇒ P = ^{3584 × 100}/₁₁₂

⇒ P = ³⁵⁸⁴⁰⁰/₁₁₂

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 3584, then the Principal = ¹⁰⁰/₁₁₂ × 3584

= ^{100 × 3584}/₁₁₂

= ³⁵⁸⁴⁰⁰/₁₁₂

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 4 years.

(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.

(4) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?

(5) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.

(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.

(7) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.

(9) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?

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