Simple Interest
Math MCQs

Question :    How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?

Correct Answer  $6750

Solution & Explanation

Solution

Given,

Amount (A) = $7762.5

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

$7762.5 = P (1 + 3% × 5)

⇒ $7762.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7762.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7762.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7762.5 = P (^{100 + 15}/₁₀₀)

⇒ $7762.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7762.5

⇒ P = ^7762.5/_¹¹⁵/100

⇒ P = 7762.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7762.5 × 100}/₁₁₅

⇒ P = ⁷⁷⁶²⁵⁰/₁₁₅

⇒ P = $6750

Thus, the sum borrowed (P) = $6750 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 7762.5, then the Principal = ¹⁰⁰/₁₁₅ × 7762.5

= ^{100 × 7762.5}/₁₁₅

= ⁷⁷⁶²⁵⁰/₁₁₅

= 6750

Thus, Principal = $6750

Thus, the sum borrowed = $6750 Answer

Similar Questions

(1) How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?

(2) If Sarah paid $4466 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 William borrowed a sum of $5500 at a rate of 3% simple interest.

(4) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?

(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.

(8) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.

(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.

(10) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.