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) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?

(2) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?

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

(4) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.

(5) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(9) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.

(10) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.