Simple Interest
Math MCQs

Question :    If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4800

Solution & Explanation

Solution

Given,

Amount (A) = $5376

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

$5376 = P (1 + 3% × 4)

⇒ $5376 = P (1 + ³/₁₀₀ × 4)

⇒ $5376 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5376 = P (1 + ¹²/₁₀₀)

⇒ $5376 = P (^{100 + 12}/₁₀₀)

⇒ $5376 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5376

⇒ P = ⁵³⁷⁶/_¹¹²/100

⇒ P = 5376 × ¹⁰⁰/₁₁₂

⇒ P = ^{5376 × 100}/₁₁₂

⇒ P = ⁵³⁷⁶⁰⁰/₁₁₂

⇒ P = $4800

Thus, the sum borrowed (P) = $4800 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 5376, then the Principal = ¹⁰⁰/₁₁₂ × 5376

= ^{100 × 5376}/₁₁₂

= ⁵³⁷⁶⁰⁰/₁₁₂

= 4800

Thus, Principal = $4800

Thus, the sum borrowed = $4800 Answer

Similar Questions

(1) In how much time a principal of $3200 will amount to $3584 at a simple interest of 4% per annum?

(2) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.

(3) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(5) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(6) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?

(8) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?