Simple Interest
Math MCQs

Question :    How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?

Correct Answer  $7800

Solution & Explanation

Solution

Given,

Amount (A) = $8580

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

$8580 = P (1 + 2% × 5)

⇒ $8580 = P (1 + ²/₁₀₀ × 5)

⇒ $8580 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8580 = P (1 + ¹⁰/₁₀₀)

⇒ $8580 = P (^{100 + 10}/₁₀₀)

⇒ $8580 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8580

⇒ P = ⁸⁵⁸⁰/_¹¹⁰/100

⇒ P = 8580 × ¹⁰⁰/₁₁₀

⇒ P = ^{8580 × 100}/₁₁₀

⇒ P = ⁸⁵⁸⁰⁰⁰/₁₁₀

⇒ P = $7800

Thus, the sum borrowed (P) = $7800 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 8580, then the Principal = ¹⁰⁰/₁₁₀ × 8580

= ^{100 × 8580}/₁₁₀

= ⁸⁵⁸⁰⁰⁰/₁₁₀

= 7800

Thus, Principal = $7800

Thus, the sum borrowed = $7800 Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.

(3) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(4) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?

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

(7) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?

(8) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.

(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?