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) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?

(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?

(4) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(5) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?

(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.

(7) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6407 to clear the loan, then find the time period of the loan.

(8) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?

(9) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.