Simple Interest
Math MCQs

Question :    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.

Correct Answer  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $4752

Rate of Simple Interest (R) = 2%

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

$4752 = P (1 + 2% × 4)

⇒ $4752 = P (1 + ²/₁₀₀ × 4)

⇒ $4752 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4752 = P (1 + ⁸/₁₀₀)

⇒ $4752 = P (^{100 + 8}/₁₀₀)

⇒ $4752 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4752

⇒ P = ⁴⁷⁵²/_¹⁰⁸/100

⇒ P = 4752 × ¹⁰⁰/₁₀₈

⇒ P = ^{4752 × 100}/₁₀₈

⇒ P = ⁴⁷⁵²⁰⁰/₁₀₈

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4752, then the Principal = ¹⁰⁰/₁₀₈ × 4752

= ^{100 × 4752}/₁₀₈

= ⁴⁷⁵²⁰⁰/₁₀₈

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(2) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?

(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.

(6) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.

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

(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.