Simple Interest
Math MCQs

Question :    How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

Correct Answer  $5300

Solution & Explanation

Solution

Given,

Amount (A) = $6095

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

$6095 = P (1 + 3% × 5)

⇒ $6095 = P (1 + ³/₁₀₀ × 5)

⇒ $6095 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6095 = P (1 + ¹⁵/₁₀₀)

⇒ $6095 = P (^{100 + 15}/₁₀₀)

⇒ $6095 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6095

⇒ P = ⁶⁰⁹⁵/_¹¹⁵/100

⇒ P = 6095 × ¹⁰⁰/₁₁₅

⇒ P = ^{6095 × 100}/₁₁₅

⇒ P = ⁶⁰⁹⁵⁰⁰/₁₁₅

⇒ P = $5300

Thus, the sum borrowed (P) = $5300 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 6095, then the Principal = ¹⁰⁰/₁₁₅ × 6095

= ^{100 × 6095}/₁₁₅

= ⁶⁰⁹⁵⁰⁰/₁₁₅

= 5300

Thus, Principal = $5300

Thus, the sum borrowed = $5300 Answer

Similar Questions

(1) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.

(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.

(7) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.

(9) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

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