Simple Interest
Math MCQs

Question :    How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?

Correct Answer  $6200

Solution & Explanation

Solution

Given,

Amount (A) = $7440

Rate of Simple Interest (R) = 4%

Time (T) = 5 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

$7440 = P (1 + 4% × 5)

⇒ $7440 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7440 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7440 = P (1 + ²⁰/₁₀₀)

⇒ $7440 = P (^{100 + 20}/₁₀₀)

⇒ $7440 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7440

⇒ P = ⁷⁴⁴⁰/_¹²⁰/100

⇒ P = 7440 × ¹⁰⁰/₁₂₀

⇒ P = ^{7440 × 100}/₁₂₀

⇒ P = ⁷⁴⁴⁰⁰⁰/₁₂₀

⇒ P = $6200

Thus, the sum borrowed (P) = $6200 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 7440, then the Principal = ¹⁰⁰/₁₂₀ × 7440

= ^{100 × 7440}/₁₂₀

= ⁷⁴⁴⁰⁰⁰/₁₂₀

= 6200

Thus, Principal = $6200

Thus, the sum borrowed = $6200 Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.

(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.

(4) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.

(7) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?

(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.

(10) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.