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) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(3) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.

(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.

(6) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?

(7) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.

(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?

(9) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.