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) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?

(2) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.

(5) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?

(8) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?

(10) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.