Simple Interest
Math MCQs

Question :    How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?

Correct Answer  $6350

Solution & Explanation

Solution

Given,

Amount (A) = $7620

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

$7620 = P (1 + 4% × 5)

⇒ $7620 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7620 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7620 = P (1 + ²⁰/₁₀₀)

⇒ $7620 = P (^{100 + 20}/₁₀₀)

⇒ $7620 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7620

⇒ P = ⁷⁶²⁰/_¹²⁰/100

⇒ P = 7620 × ¹⁰⁰/₁₂₀

⇒ P = ^{7620 × 100}/₁₂₀

⇒ P = ⁷⁶²⁰⁰⁰/₁₂₀

⇒ P = $6350

Thus, the sum borrowed (P) = $6350 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 7620, then the Principal = ¹⁰⁰/₁₂₀ × 7620

= ^{100 × 7620}/₁₂₀

= ⁷⁶²⁰⁰⁰/₁₂₀

= 6350

Thus, Principal = $6350

Thus, the sum borrowed = $6350 Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.

(2) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

(3) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.

(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?

(5) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.

(7) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.