Simple Interest
Math MCQs

Question :    If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4200

Solution & Explanation

Solution

Given,

Amount (A) = $4704

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

$4704 = P (1 + 3% × 4)

⇒ $4704 = P (1 + ³/₁₀₀ × 4)

⇒ $4704 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4704 = P (1 + ¹²/₁₀₀)

⇒ $4704 = P (^{100 + 12}/₁₀₀)

⇒ $4704 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4704

⇒ P = ⁴⁷⁰⁴/_¹¹²/100

⇒ P = 4704 × ¹⁰⁰/₁₁₂

⇒ P = ^{4704 × 100}/₁₁₂

⇒ P = ⁴⁷⁰⁴⁰⁰/₁₁₂

⇒ 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 = 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 4704, then the Principal = ¹⁰⁰/₁₁₂ × 4704

= ^{100 × 4704}/₁₁₂

= ⁴⁷⁰⁴⁰⁰/₁₁₂

= 4200

Thus, Principal = $4200

Thus, the sum borrowed = $4200 Answer

Similar Questions

(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 9% simple interest?

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.

(3) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.

(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?

(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.

(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.