Simple Interest
Math MCQs

Question :    If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5510

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

$5510 = P (1 + 4% × 4)

⇒ $5510 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5510 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5510 = P (1 + ¹⁶/₁₀₀)

⇒ $5510 = P (^{100 + 16}/₁₀₀)

⇒ $5510 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5510

⇒ P = ⁵⁵¹⁰/_¹¹⁶/100

⇒ P = 5510 × ¹⁰⁰/₁₁₆

⇒ P = ^{5510 × 100}/₁₁₆

⇒ P = ⁵⁵¹⁰⁰⁰/₁₁₆

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5510, then the Principal = ¹⁰⁰/₁₁₆ × 5510

= ^{100 × 5510}/₁₁₆

= ⁵⁵¹⁰⁰⁰/₁₁₆

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

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

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

(4) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?

(5) 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.

(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 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) 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?