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) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.

(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?

(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.

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

(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.

(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

(9) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.