Simple Interest
Math MCQs

Question :    Steven had to pay $5152 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  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5152

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

$5152 = P (1 + 4% × 3)

⇒ $5152 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5152 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5152 = P (1 + ¹²/₁₀₀)

⇒ $5152 = P (^{100 + 12}/₁₀₀)

⇒ $5152 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5152

⇒ P = ⁵¹⁵²/_¹¹²/100

⇒ P = 5152 × ¹⁰⁰/₁₁₂

⇒ P = ^{5152 × 100}/₁₁₂

⇒ P = ⁵¹⁵²⁰⁰/₁₁₂

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 5152, then the Principal = ¹⁰⁰/₁₁₂ × 5152

= ^{100 × 5152}/₁₁₂

= ⁵¹⁵²⁰⁰/₁₁₂

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(3) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?

(5) 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.

(6) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(8) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.

(9) If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

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