Simple Interest
Math MCQs

Question :    How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?

Correct Answer  $8000

Solution & Explanation

Solution

Given,

Amount (A) = $8800

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

$8800 = P (1 + 2% × 5)

⇒ $8800 = P (1 + ²/₁₀₀ × 5)

⇒ $8800 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8800 = P (1 + ¹⁰/₁₀₀)

⇒ $8800 = P (^{100 + 10}/₁₀₀)

⇒ $8800 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8800

⇒ P = ⁸⁸⁰⁰/_¹¹⁰/100

⇒ P = 8800 × ¹⁰⁰/₁₁₀

⇒ P = ^{8800 × 100}/₁₁₀

⇒ P = ⁸⁸⁰⁰⁰⁰/₁₁₀

⇒ P = $8000

Thus, the sum borrowed (P) = $8000 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 8800, then the Principal = ¹⁰⁰/₁₁₀ × 8800

= ^{100 × 8800}/₁₁₀

= ⁸⁸⁰⁰⁰⁰/₁₁₀

= 8000

Thus, Principal = $8000

Thus, the sum borrowed = $8000 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.

(3) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.

(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.

(7) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?

(8) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?

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