Simple Interest
Math MCQs

Question :    How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?

Correct Answer  $6850

Solution & Explanation

Solution

Given,

Amount (A) = $7877.5

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

$7877.5 = P (1 + 3% × 5)

⇒ $7877.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7877.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7877.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7877.5 = P (^{100 + 15}/₁₀₀)

⇒ $7877.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7877.5

⇒ P = ^7877.5/_¹¹⁵/100

⇒ P = 7877.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7877.5 × 100}/₁₁₅

⇒ P = ⁷⁸⁷⁷⁵⁰/₁₁₅

⇒ P = $6850

Thus, the sum borrowed (P) = $6850 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 7877.5, then the Principal = ¹⁰⁰/₁₁₅ × 7877.5

= ^{100 × 7877.5}/₁₁₅

= ⁷⁸⁷⁷⁵⁰/₁₁₅

= 6850

Thus, Principal = $6850

Thus, the sum borrowed = $6850 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.

(4) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.

(6) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(7) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?

(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.

(9) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.