Simple Interest
Math MCQs

Question :    William had to pay $3710 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  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $3710

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

$3710 = P (1 + 2% × 3)

⇒ $3710 = P (1 + ²/₁₀₀ × 3)

⇒ $3710 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3710 = P (1 + ⁶/₁₀₀)

⇒ $3710 = P (^{100 + 6}/₁₀₀)

⇒ $3710 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3710

⇒ P = ³⁷¹⁰/_¹⁰⁶/100

⇒ P = 3710 × ¹⁰⁰/₁₀₆

⇒ P = ^{3710 × 100}/₁₀₆

⇒ P = ³⁷¹⁰⁰⁰/₁₀₆

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 3710, then the Principal = ¹⁰⁰/₁₀₆ × 3710

= ^{100 × 3710}/₁₀₆

= ³⁷¹⁰⁰⁰/₁₀₆

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.

(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.

(5) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?

(7) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?

(9) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.