Simple Interest
Math MCQs

Question :    If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $4928

Rate of Simple Interest (R) = 3%

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

$4928 = P (1 + 3% × 4)

⇒ $4928 = P (1 + ³/₁₀₀ × 4)

⇒ $4928 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4928 = P (1 + ¹²/₁₀₀)

⇒ $4928 = P (^{100 + 12}/₁₀₀)

⇒ $4928 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4928

⇒ P = ⁴⁹²⁸/_¹¹²/100

⇒ P = 4928 × ¹⁰⁰/₁₁₂

⇒ P = ^{4928 × 100}/₁₁₂

⇒ P = ⁴⁹²⁸⁰⁰/₁₁₂

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 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 4928, then the Principal = ¹⁰⁰/₁₁₂ × 4928

= ^{100 × 4928}/₁₁₂

= ⁴⁹²⁸⁰⁰/₁₁₂

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(2) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(3) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?

(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?

(7) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

(9) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.