Simple Interest
Math MCQs

Question :    How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

Correct Answer  $7600

Solution & Explanation

Solution

Given,

Amount (A) = $8360

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

$8360 = P (1 + 2% × 5)

⇒ $8360 = P (1 + ²/₁₀₀ × 5)

⇒ $8360 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8360 = P (1 + ¹⁰/₁₀₀)

⇒ $8360 = P (^{100 + 10}/₁₀₀)

⇒ $8360 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8360

⇒ P = ⁸³⁶⁰/_¹¹⁰/100

⇒ P = 8360 × ¹⁰⁰/₁₁₀

⇒ P = ^{8360 × 100}/₁₁₀

⇒ P = ⁸³⁶⁰⁰⁰/₁₁₀

⇒ P = $7600

Thus, the sum borrowed (P) = $7600 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 8360, then the Principal = ¹⁰⁰/₁₁₀ × 8360

= ^{100 × 8360}/₁₁₀

= ⁸³⁶⁰⁰⁰/₁₁₀

= 7600

Thus, Principal = $7600

Thus, the sum borrowed = $7600 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) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?

(3) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?

(4) If William paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.

(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.

(8) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.

(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(10) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.