Simple Interest
Math MCQs

Question :    If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4200

Solution & Explanation

Solution

Given,

Amount (A) = $4872

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

$4872 = P (1 + 4% × 4)

⇒ $4872 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4872 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4872 = P (1 + ¹⁶/₁₀₀)

⇒ $4872 = P (^{100 + 16}/₁₀₀)

⇒ $4872 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4872

⇒ P = ⁴⁸⁷²/_¹¹⁶/100

⇒ P = 4872 × ¹⁰⁰/₁₁₆

⇒ P = ^{4872 × 100}/₁₁₆

⇒ P = ⁴⁸⁷²⁰⁰/₁₁₆

⇒ P = $4200

Thus, the sum borrowed (P) = $4200 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 4872, then the Principal = ¹⁰⁰/₁₁₆ × 4872

= ^{100 × 4872}/₁₁₆

= ⁴⁸⁷²⁰⁰/₁₁₆

= 4200

Thus, Principal = $4200

Thus, the sum borrowed = $4200 Answer

Similar Questions

(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?

(2) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?

(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(4) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(6) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.

(8) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?

(9) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.