Simple Interest
Math MCQs

Question :    If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5684

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

$5684 = P (1 + 4% × 4)

⇒ $5684 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5684 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5684 = P (1 + ¹⁶/₁₀₀)

⇒ $5684 = P (^{100 + 16}/₁₀₀)

⇒ $5684 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5684

⇒ P = ⁵⁶⁸⁴/_¹¹⁶/100

⇒ P = 5684 × ¹⁰⁰/₁₁₆

⇒ P = ^{5684 × 100}/₁₁₆

⇒ P = ⁵⁶⁸⁴⁰⁰/₁₁₆

⇒ P = $4900

Thus, the sum borrowed (P) = $4900 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 5684, then the Principal = ¹⁰⁰/₁₁₆ × 5684

= ^{100 × 5684}/₁₁₆

= ⁵⁶⁸⁴⁰⁰/₁₁₆

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.

(3) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(6) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?

(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?

(8) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?

(9) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(10) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.