Simple Interest
Math MCQs

Question :    If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $5640

Rate of Simple Interest (R) = 5%

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

$5640 = P (1 + 5% × 4)

⇒ $5640 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5640 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5640 = P (1 + ²⁰/₁₀₀)

⇒ $5640 = P (^{100 + 20}/₁₀₀)

⇒ $5640 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5640

⇒ P = ⁵⁶⁴⁰/_¹²⁰/100

⇒ P = 5640 × ¹⁰⁰/₁₂₀

⇒ P = ^{5640 × 100}/₁₂₀

⇒ P = ⁵⁶⁴⁰⁰⁰/₁₂₀

⇒ P = $4700

Thus, the sum borrowed (P) = $4700 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 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 5640, then the Principal = ¹⁰⁰/₁₂₀ × 5640

= ^{100 × 5640}/₁₂₀

= ⁵⁶⁴⁰⁰⁰/₁₂₀

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.

(2) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.

(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(4) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.

(6) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 7 years.

(8) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?

(9) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.