Simple Interest
Math MCQs

Question :    How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?

Correct Answer  $6500

Solution & Explanation

Solution

Given,

Amount (A) = $8125

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

$8125 = P (1 + 5% × 5)

⇒ $8125 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8125 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8125 = P (1 + ²⁵/₁₀₀)

⇒ $8125 = P (^{100 + 25}/₁₀₀)

⇒ $8125 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8125

⇒ P = ⁸¹²⁵/_¹²⁵/100

⇒ P = 8125 × ¹⁰⁰/₁₂₅

⇒ P = ^{8125 × 100}/₁₂₅

⇒ P = ⁸¹²⁵⁰⁰/₁₂₅

⇒ P = $6500

Thus, the sum borrowed (P) = $6500 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 8125, then the Principal = ¹⁰⁰/₁₂₅ × 8125

= ^{100 × 8125}/₁₂₅

= ⁸¹²⁵⁰⁰/₁₂₅

= 6500

Thus, Principal = $6500

Thus, the sum borrowed = $6500 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.

(3) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?

(4) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.

(5) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.

(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?

(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(10) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.