Simple Interest
Math MCQs

Question :    Emily had to pay $5035 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  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5035

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

$5035 = P (1 + 2% × 3)

⇒ $5035 = P (1 + ²/₁₀₀ × 3)

⇒ $5035 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $5035 = P (1 + ⁶/₁₀₀)

⇒ $5035 = P (^{100 + 6}/₁₀₀)

⇒ $5035 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $5035

⇒ P = ⁵⁰³⁵/_¹⁰⁶/100

⇒ P = 5035 × ¹⁰⁰/₁₀₆

⇒ P = ^{5035 × 100}/₁₀₆

⇒ P = ⁵⁰³⁵⁰⁰/₁₀₆

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5035, then the Principal = ¹⁰⁰/₁₀₆ × 5035

= ^{100 × 5035}/₁₀₆

= ⁵⁰³⁵⁰⁰/₁₀₆

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.

(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.

(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.

(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.

(7) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.

(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(10) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.