Simple Interest
Math MCQs

Question :    If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4950

Solution & Explanation

Solution

Given,

Amount (A) = $5742

Rate of Simple Interest (R) = 4%

Time (T) = 4 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

$5742 = P (1 + 4% × 4)

⇒ $5742 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5742 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5742 = P (1 + ¹⁶/₁₀₀)

⇒ $5742 = P (^{100 + 16}/₁₀₀)

⇒ $5742 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5742

⇒ P = ⁵⁷⁴²/_¹¹⁶/100

⇒ P = 5742 × ¹⁰⁰/₁₁₆

⇒ P = ^{5742 × 100}/₁₁₆

⇒ P = ⁵⁷⁴²⁰⁰/₁₁₆

⇒ P = $4950

Thus, the sum borrowed (P) = $4950 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 5742, then the Principal = ¹⁰⁰/₁₁₆ × 5742

= ^{100 × 5742}/₁₁₆

= ⁵⁷⁴²⁰⁰/₁₁₆

= 4950

Thus, Principal = $4950

Thus, the sum borrowed = $4950 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(2) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?

(4) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(5) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

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

(7) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 3 years.

(8) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(10) 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.