Simple Interest
Math MCQs

Question :    If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5626

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

$5626 = P (1 + 4% × 4)

⇒ $5626 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5626 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5626 = P (1 + ¹⁶/₁₀₀)

⇒ $5626 = P (^{100 + 16}/₁₀₀)

⇒ $5626 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5626

⇒ P = ⁵⁶²⁶/_¹¹⁶/100

⇒ P = 5626 × ¹⁰⁰/₁₁₆

⇒ P = ^{5626 × 100}/₁₁₆

⇒ P = ⁵⁶²⁶⁰⁰/₁₁₆

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5626, then the Principal = ¹⁰⁰/₁₁₆ × 5626

= ^{100 × 5626}/₁₁₆

= ⁵⁶²⁶⁰⁰/₁₁₆

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(2) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?

(3) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?

(5) If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.

(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(8) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(9) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?

(10) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.