Simple Interest
Math MCQs

Question :    David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $3706

Rate of Simple Interest (R) = 3%

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

$3706 = P (1 + 3% × 3)

⇒ $3706 = P (1 + ³/₁₀₀ × 3)

⇒ $3706 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3706 = P (1 + ⁹/₁₀₀)

⇒ $3706 = P (^{100 + 9}/₁₀₀)

⇒ $3706 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3706

⇒ P = ³⁷⁰⁶/_¹⁰⁹/100

⇒ P = 3706 × ¹⁰⁰/₁₀₉

⇒ P = ^{3706 × 100}/₁₀₉

⇒ P = ³⁷⁰⁶⁰⁰/₁₀₉

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 3706, then the Principal = ¹⁰⁰/₁₀₉ × 3706

= ^{100 × 3706}/₁₀₉

= ³⁷⁰⁶⁰⁰/₁₀₉

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?

(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.

(3) Nancy had to pay $4772.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.

(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

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

(7) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.

(9) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.