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) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.

(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?

(3) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

(4) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(5) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?

(6) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.

(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?

(8) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.

(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?

(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?