Simple Interest
Math MCQs

Question :    How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?

Correct Answer  $5550

Solution & Explanation

Solution

Given,

Amount (A) = $6937.5

Rate of Simple Interest (R) = 5%

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

$6937.5 = P (1 + 5% × 5)

⇒ $6937.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6937.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6937.5 = P (1 + ²⁵/₁₀₀)

⇒ $6937.5 = P (^{100 + 25}/₁₀₀)

⇒ $6937.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6937.5

⇒ P = ^6937.5/_¹²⁵/100

⇒ P = 6937.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{6937.5 × 100}/₁₂₅

⇒ P = ⁶⁹³⁷⁵⁰/₁₂₅

⇒ P = $5550

Thus, the sum borrowed (P) = $5550 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 6937.5, then the Principal = ¹⁰⁰/₁₂₅ × 6937.5

= ^{100 × 6937.5}/₁₂₅

= ⁶⁹³⁷⁵⁰/₁₂₅

= 5550

Thus, Principal = $5550

Thus, the sum borrowed = $5550 Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

(2) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?

(5) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.

(6) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.

(7) How much loan did Donald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7150 to clear it?

(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?

(9) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 7 years.