Simple Interest
Math MCQs

Question :    How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?

Correct Answer  $7600

Solution & Explanation

Solution

Given,

Amount (A) = $8740

Rate of Simple Interest (R) = 3%

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

$8740 = P (1 + 3% × 5)

⇒ $8740 = P (1 + ³/₁₀₀ × 5)

⇒ $8740 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8740 = P (1 + ¹⁵/₁₀₀)

⇒ $8740 = P (^{100 + 15}/₁₀₀)

⇒ $8740 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8740

⇒ P = ⁸⁷⁴⁰/_¹¹⁵/100

⇒ P = 8740 × ¹⁰⁰/₁₁₅

⇒ P = ^{8740 × 100}/₁₁₅

⇒ P = ⁸⁷⁴⁰⁰⁰/₁₁₅

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 8740, then the Principal = ¹⁰⁰/₁₁₅ × 8740

= ^{100 × 8740}/₁₁₅

= ⁸⁷⁴⁰⁰⁰/₁₁₅

= 7600

Thus, Principal = $7600

Thus, the sum borrowed = $7600 Answer

Similar Questions

(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?

(2) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.

(4) If Nancy paid $4482 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.

(7) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?

(9) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.