Simple Interest
Math MCQs

Question :    Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4200

Solution & Explanation

Solution

Given,

Amount (A) = $4704

Rate of Simple Interest (R) = 4%

Time (T) = 3 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 + 4% × 3)

⇒ $4704 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4704 = P (1 + ^{4 × 3}/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 = 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(3) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.

(6) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?

(7) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(8) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.