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) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(2) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.

(4) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?

(5) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?

(6) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.

(8) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?

(10) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.