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) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?

(2) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.

(3) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.

(5) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 4% simple interest?

(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(9) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(10) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.