Simple Interest
Math MCQs

Question :    Robert had to pay $3472 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  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3472

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

$3472 = P (1 + 4% × 3)

⇒ $3472 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3472 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3472 = P (1 + ¹²/₁₀₀)

⇒ $3472 = P (^{100 + 12}/₁₀₀)

⇒ $3472 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3472

⇒ P = ³⁴⁷²/_¹¹²/100

⇒ P = 3472 × ¹⁰⁰/₁₁₂

⇒ P = ^{3472 × 100}/₁₁₂

⇒ P = ³⁴⁷²⁰⁰/₁₁₂

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 3472, then the Principal = ¹⁰⁰/₁₁₂ × 3472

= ^{100 × 3472}/₁₁₂

= ³⁴⁷²⁰⁰/₁₁₂

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 8% simple interest?

(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(4) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.

(5) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?

(7) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.

(8) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?

(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.

(10) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.