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) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.

(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(3) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

(4) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.

(6) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 4 years.

(8) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.