Simple Interest
Math MCQs

Question :    How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?

Correct Answer  $7400

Solution & Explanation

Solution

Given,

Amount (A) = $8510

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

$8510 = P (1 + 3% × 5)

⇒ $8510 = P (1 + ³/₁₀₀ × 5)

⇒ $8510 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8510 = P (1 + ¹⁵/₁₀₀)

⇒ $8510 = P (^{100 + 15}/₁₀₀)

⇒ $8510 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8510

⇒ P = ⁸⁵¹⁰/_¹¹⁵/100

⇒ P = 8510 × ¹⁰⁰/₁₁₅

⇒ P = ^{8510 × 100}/₁₁₅

⇒ P = ⁸⁵¹⁰⁰⁰/₁₁₅

⇒ P = $7400

Thus, the sum borrowed (P) = $7400 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 8510, then the Principal = ¹⁰⁰/₁₁₅ × 8510

= ^{100 × 8510}/₁₁₅

= ⁸⁵¹⁰⁰⁰/₁₁₅

= 7400

Thus, Principal = $7400

Thus, the sum borrowed = $7400 Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.

(5) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

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

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.

(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.

(10) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.