Simple Interest
Math MCQs

Question :    How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?

Correct Answer  $6200

Solution & Explanation

Solution

Given,

Amount (A) = $6820

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

$6820 = P (1 + 2% × 5)

⇒ $6820 = P (1 + ²/₁₀₀ × 5)

⇒ $6820 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6820 = P (1 + ¹⁰/₁₀₀)

⇒ $6820 = P (^{100 + 10}/₁₀₀)

⇒ $6820 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6820

⇒ P = ⁶⁸²⁰/_¹¹⁰/100

⇒ P = 6820 × ¹⁰⁰/₁₁₀

⇒ P = ^{6820 × 100}/₁₁₀

⇒ P = ⁶⁸²⁰⁰⁰/₁₁₀

⇒ P = $6200

Thus, the sum borrowed (P) = $6200 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 6820, then the Principal = ¹⁰⁰/₁₁₀ × 6820

= ^{100 × 6820}/₁₁₀

= ⁶⁸²⁰⁰⁰/₁₁₀

= 6200

Thus, Principal = $6200

Thus, the sum borrowed = $6200 Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(2) Sandra took a loan of $6900 at the rate of 6% 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 if William borrowed a sum of $3500 at 6% simple interest for 3 years.

(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(5) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(7) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?

(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?