Simple Interest
Math MCQs

Question :    If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $5046

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

$5046 = P (1 + 4% × 4)

⇒ $5046 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5046 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5046 = P (1 + ¹⁶/₁₀₀)

⇒ $5046 = P (^{100 + 16}/₁₀₀)

⇒ $5046 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5046

⇒ P = ⁵⁰⁴⁶/_¹¹⁶/100

⇒ P = 5046 × ¹⁰⁰/₁₁₆

⇒ P = ^{5046 × 100}/₁₁₆

⇒ P = ⁵⁰⁴⁶⁰⁰/₁₁₆

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 5046, then the Principal = ¹⁰⁰/₁₁₆ × 5046

= ^{100 × 5046}/₁₁₆

= ⁵⁰⁴⁶⁰⁰/₁₁₆

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.

(2) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?

(4) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.

(5) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

(7) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(9) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.