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) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(3) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?

(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

(7) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.

(9) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.