Simple Interest
Math MCQs

Question :  ( 1 of 10 )  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.

Correct Answer  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3584

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

$3584 = P (1 + 3% × 4)

⇒ $3584 = P (1 + ³/₁₀₀ × 4)

⇒ $3584 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3584 = P (1 + ¹²/₁₀₀)

⇒ $3584 = P (^{100 + 12}/₁₀₀)

⇒ $3584 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3584

⇒ P = ³⁵⁸⁴/_¹¹²/100

⇒ P = 3584 × ¹⁰⁰/₁₁₂

⇒ P = ^{3584 × 100}/₁₁₂

⇒ P = ³⁵⁸⁴⁰⁰/₁₁₂

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 3584, then the Principal = ¹⁰⁰/₁₁₂ × 3584

= ^{100 × 3584}/₁₁₂

= ³⁵⁸⁴⁰⁰/₁₁₂

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.

(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.

(5) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.

(7) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?

(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?