Simple Interest
Math MCQs

Question :    How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?

Correct Answer  $5900

Solution & Explanation

Solution

Given,

Amount (A) = $6785

Rate of Simple Interest (R) = 3%

Time (T) = 5 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

$6785 = P (1 + 3% × 5)

⇒ $6785 = P (1 + ³/₁₀₀ × 5)

⇒ $6785 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6785 = P (1 + ¹⁵/₁₀₀)

⇒ $6785 = P (^{100 + 15}/₁₀₀)

⇒ $6785 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6785

⇒ P = ⁶⁷⁸⁵/_¹¹⁵/100

⇒ P = 6785 × ¹⁰⁰/₁₁₅

⇒ P = ^{6785 × 100}/₁₁₅

⇒ P = ⁶⁷⁸⁵⁰⁰/₁₁₅

⇒ P = $5900

Thus, the sum borrowed (P) = $5900 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6785, then the Principal = ¹⁰⁰/₁₁₅ × 6785

= ^{100 × 6785}/₁₁₅

= ⁶⁷⁸⁵⁰⁰/₁₁₅

= 5900

Thus, Principal = $5900

Thus, the sum borrowed = $5900 Answer

Similar Questions

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

(2) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.

(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(5) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.

(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.

(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 8 years.