Simple Interest
Math MCQs

Question :    How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?

Correct Answer  $5300

Solution & Explanation

Solution

Given,

Amount (A) = $5830

Rate of Simple Interest (R) = 2%

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

$5830 = P (1 + 2% × 5)

⇒ $5830 = P (1 + ²/₁₀₀ × 5)

⇒ $5830 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5830 = P (1 + ¹⁰/₁₀₀)

⇒ $5830 = P (^{100 + 10}/₁₀₀)

⇒ $5830 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5830

⇒ P = ⁵⁸³⁰/_¹¹⁰/100

⇒ P = 5830 × ¹⁰⁰/₁₁₀

⇒ P = ^{5830 × 100}/₁₁₀

⇒ P = ⁵⁸³⁰⁰⁰/₁₁₀

⇒ 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 5830, then the Principal = ¹⁰⁰/₁₁₀ × 5830

= ^{100 × 5830}/₁₁₀

= ⁵⁸³⁰⁰⁰/₁₁₀

= 5300

Thus, Principal = $5300

Thus, the sum borrowed = $5300 Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.

(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(3) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.

(7) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.

(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.

(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?