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) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.

(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?

(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.

(5) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(6) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.

(9) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?

(10) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.