Simple Interest
Math MCQs

Question :    How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?

Correct Answer  $5100

Solution & Explanation

Solution

Given,

Amount (A) = $6375

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

$6375 = P (1 + 5% × 5)

⇒ $6375 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6375 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6375 = P (1 + ²⁵/₁₀₀)

⇒ $6375 = P (^{100 + 25}/₁₀₀)

⇒ $6375 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6375

⇒ P = ⁶³⁷⁵/_¹²⁵/100

⇒ P = 6375 × ¹⁰⁰/₁₂₅

⇒ P = ^{6375 × 100}/₁₂₅

⇒ P = ⁶³⁷⁵⁰⁰/₁₂₅

⇒ P = $5100

Thus, the sum borrowed (P) = $5100 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 6375, then the Principal = ¹⁰⁰/₁₂₅ × 6375

= ^{100 × 6375}/₁₂₅

= ⁶³⁷⁵⁰⁰/₁₂₅

= 5100

Thus, Principal = $5100

Thus, the sum borrowed = $5100 Answer

Similar Questions

(1) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.

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

(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?

(5) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(7) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.

(9) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.