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) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.

(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.

(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.

(7) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.

(9) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?

(10) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.