Simple Interest
Math MCQs

Question :    If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $5278

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

$5278 = P (1 + 4% × 4)

⇒ $5278 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5278 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5278 = P (1 + ¹⁶/₁₀₀)

⇒ $5278 = P (^{100 + 16}/₁₀₀)

⇒ $5278 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5278

⇒ P = ⁵²⁷⁸/_¹¹⁶/100

⇒ P = 5278 × ¹⁰⁰/₁₁₆

⇒ P = ^{5278 × 100}/₁₁₆

⇒ P = ⁵²⁷⁸⁰⁰/₁₁₆

⇒ P = $4550

Thus, the sum borrowed (P) = $4550 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 5278, then the Principal = ¹⁰⁰/₁₁₆ × 5278

= ^{100 × 5278}/₁₁₆

= ⁵²⁷⁸⁰⁰/₁₁₆

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.

(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.

(3) Christopher had to pay $4360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.

(5) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.

(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(8) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.

(9) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?

(10) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?