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) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

(4) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.

(6) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(7) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.

(9) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.