Simple Interest
Math MCQs

Question :    If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5292

Rate of Simple Interest (R) = 2%

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

$5292 = P (1 + 2% × 4)

⇒ $5292 = P (1 + ²/₁₀₀ × 4)

⇒ $5292 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $5292 = P (1 + ⁸/₁₀₀)

⇒ $5292 = P (^{100 + 8}/₁₀₀)

⇒ $5292 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $5292

⇒ P = ⁵²⁹²/_¹⁰⁸/100

⇒ P = 5292 × ¹⁰⁰/₁₀₈

⇒ P = ^{5292 × 100}/₁₀₈

⇒ P = ⁵²⁹²⁰⁰/₁₀₈

⇒ 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 5292, then the Principal = ¹⁰⁰/₁₀₈ × 5292

= ^{100 × 5292}/₁₀₈

= ⁵²⁹²⁰⁰/₁₀₈

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.

(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.

(5) 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.

(6) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.

(8) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

(9) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.