Simple Interest
Math MCQs

Question :    If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4800

Solution & Explanation

Solution

Given,

Amount (A) = $5568

Rate of Simple Interest (R) = 4%

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

$5568 = P (1 + 4% × 4)

⇒ $5568 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5568 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5568 = P (1 + ¹⁶/₁₀₀)

⇒ $5568 = P (^{100 + 16}/₁₀₀)

⇒ $5568 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5568

⇒ P = ⁵⁵⁶⁸/_¹¹⁶/100

⇒ P = 5568 × ¹⁰⁰/₁₁₆

⇒ P = ^{5568 × 100}/₁₁₆

⇒ P = ⁵⁵⁶⁸⁰⁰/₁₁₆

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 5568, then the Principal = ¹⁰⁰/₁₁₆ × 5568

= ^{100 × 5568}/₁₁₆

= ⁵⁵⁶⁸⁰⁰/₁₁₆

= 4800

Thus, Principal = $4800

Thus, the sum borrowed = $4800 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.

(2) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.

(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?

(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.

(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(7) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.

(9) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.

(10) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.