Simple Interest
Math MCQs

Question :    James had to pay $3360 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  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3360

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

$3360 = P (1 + 4% × 3)

⇒ $3360 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3360 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3360 = P (1 + ¹²/₁₀₀)

⇒ $3360 = P (^{100 + 12}/₁₀₀)

⇒ $3360 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3360

⇒ P = ³³⁶⁰/_¹¹²/100

⇒ P = 3360 × ¹⁰⁰/₁₁₂

⇒ P = ^{3360 × 100}/₁₁₂

⇒ P = ³³⁶⁰⁰⁰/₁₁₂

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3360, then the Principal = ¹⁰⁰/₁₁₂ × 3360

= ^{100 × 3360}/₁₁₂

= ³³⁶⁰⁰⁰/₁₁₂

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?

(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?

(4) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.

(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(8) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.