Simple Interest
Math MCQs

Question :    How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?

Correct Answer  $7850

Solution & Explanation

Solution

Given,

Amount (A) = $9027.5

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

$9027.5 = P (1 + 3% × 5)

⇒ $9027.5 = P (1 + ³/₁₀₀ × 5)

⇒ $9027.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $9027.5 = P (1 + ¹⁵/₁₀₀)

⇒ $9027.5 = P (^{100 + 15}/₁₀₀)

⇒ $9027.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $9027.5

⇒ P = ^9027.5/_¹¹⁵/100

⇒ P = 9027.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{9027.5 × 100}/₁₁₅

⇒ P = ⁹⁰²⁷⁵⁰/₁₁₅

⇒ P = $7850

Thus, the sum borrowed (P) = $7850 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 9027.5, then the Principal = ¹⁰⁰/₁₁₅ × 9027.5

= ^{100 × 9027.5}/₁₁₅

= ⁹⁰²⁷⁵⁰/₁₁₅

= 7850

Thus, Principal = $7850

Thus, the sum borrowed = $7850 Answer

Similar Questions

(1) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?

(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.

(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?

(4) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.

(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.

(7) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

(10) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.