Simple Interest
Math MCQs

Question :    How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?

Correct Answer  $5800

Solution & Explanation

Solution

Given,

Amount (A) = $6380

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

$6380 = P (1 + 2% × 5)

⇒ $6380 = P (1 + ²/₁₀₀ × 5)

⇒ $6380 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6380 = P (1 + ¹⁰/₁₀₀)

⇒ $6380 = P (^{100 + 10}/₁₀₀)

⇒ $6380 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6380

⇒ P = ⁶³⁸⁰/_¹¹⁰/100

⇒ P = 6380 × ¹⁰⁰/₁₁₀

⇒ P = ^{6380 × 100}/₁₁₀

⇒ P = ⁶³⁸⁰⁰⁰/₁₁₀

⇒ P = $5800

Thus, the sum borrowed (P) = $5800 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 6380, then the Principal = ¹⁰⁰/₁₁₀ × 6380

= ^{100 × 6380}/₁₁₀

= ⁶³⁸⁰⁰⁰/₁₁₀

= 5800

Thus, Principal = $5800

Thus, the sum borrowed = $5800 Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(2) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.

(3) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

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

(6) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(7) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 3 years.

(10) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.