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) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.

(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.

(4) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.

(6) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(8) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

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