Simple Interest
Math MCQs

Question :    Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4900

Solution & Explanation

Solution

Given,

Amount (A) = $5488

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$5488 = P (1 + 4% × 3)

⇒ $5488 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5488 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5488 = P (1 + ¹²/₁₀₀)

⇒ $5488 = P (^{100 + 12}/₁₀₀)

⇒ $5488 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5488

⇒ P = ⁵⁴⁸⁸/_¹¹²/100

⇒ P = 5488 × ¹⁰⁰/₁₁₂

⇒ P = ^{5488 × 100}/₁₁₂

⇒ P = ⁵⁴⁸⁸⁰⁰/₁₁₂

⇒ 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 5488, then the Principal = ¹⁰⁰/₁₁₂ × 5488

= ^{100 × 5488}/₁₁₂

= ⁵⁴⁸⁸⁰⁰/₁₁₂

= 4900

Thus, Principal = $4900

Thus, the sum borrowed = $4900 Answer

Similar Questions

(1) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 7 years.

(3) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(4) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.

(7) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.

(10) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.