Simple Interest
Math MCQs

Question :    If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $5264

Rate of Simple Interest (R) = 3%

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

$5264 = P (1 + 3% × 4)

⇒ $5264 = P (1 + ³/₁₀₀ × 4)

⇒ $5264 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5264 = P (1 + ¹²/₁₀₀)

⇒ $5264 = P (^{100 + 12}/₁₀₀)

⇒ $5264 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5264

⇒ P = ⁵²⁶⁴/_¹¹²/100

⇒ P = 5264 × ¹⁰⁰/₁₁₂

⇒ P = ^{5264 × 100}/₁₁₂

⇒ P = ⁵²⁶⁴⁰⁰/₁₁₂

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 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 5264, then the Principal = ¹⁰⁰/₁₁₂ × 5264

= ^{100 × 5264}/₁₁₂

= ⁵²⁶⁴⁰⁰/₁₁₂

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.

(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(4) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(7) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?

(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.

(9) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.