Simple Interest
Math MCQs

Question :    Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3450

Solution & Explanation

Solution

Given,

Amount (A) = $3657

Rate of Simple Interest (R) = 2%

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

$3657 = P (1 + 2% × 3)

⇒ $3657 = P (1 + ²/₁₀₀ × 3)

⇒ $3657 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3657 = P (1 + ⁶/₁₀₀)

⇒ $3657 = P (^{100 + 6}/₁₀₀)

⇒ $3657 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3657

⇒ P = ³⁶⁵⁷/_¹⁰⁶/100

⇒ P = 3657 × ¹⁰⁰/₁₀₆

⇒ P = ^{3657 × 100}/₁₀₆

⇒ P = ³⁶⁵⁷⁰⁰/₁₀₆

⇒ P = $3450

Thus, the sum borrowed (P) = $3450 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 = 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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3657, then the Principal = ¹⁰⁰/₁₀₆ × 3657

= ^{100 × 3657}/₁₀₆

= ³⁶⁵⁷⁰⁰/₁₀₆

= 3450

Thus, Principal = $3450

Thus, the sum borrowed = $3450 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?

(4) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?

(6) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?

(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

(10) 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.