Simple Interest
Math MCQs

Question :    How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?

Correct Answer  $7100

Solution & Explanation

Solution

Given,

Amount (A) = $8165

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

$8165 = P (1 + 3% × 5)

⇒ $8165 = P (1 + ³/₁₀₀ × 5)

⇒ $8165 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8165 = P (1 + ¹⁵/₁₀₀)

⇒ $8165 = P (^{100 + 15}/₁₀₀)

⇒ $8165 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8165

⇒ P = ⁸¹⁶⁵/_¹¹⁵/100

⇒ P = 8165 × ¹⁰⁰/₁₁₅

⇒ P = ^{8165 × 100}/₁₁₅

⇒ P = ⁸¹⁶⁵⁰⁰/₁₁₅

⇒ P = $7100

Thus, the sum borrowed (P) = $7100 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 8165, then the Principal = ¹⁰⁰/₁₁₅ × 8165

= ^{100 × 8165}/₁₁₅

= ⁸¹⁶⁵⁰⁰/₁₁₅

= 7100

Thus, Principal = $7100

Thus, the sum borrowed = $7100 Answer

Similar Questions

(1) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?

(2) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?

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

(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.

(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.

(7) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?

(8) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.

(10) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?