Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?

Correct Answer  $7300

Solution & Explanation

Solution

Given,

Amount (A) = $8395

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

$8395 = P (1 + 3% × 5)

⇒ $8395 = P (1 + ³/₁₀₀ × 5)

⇒ $8395 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8395 = P (1 + ¹⁵/₁₀₀)

⇒ $8395 = P (^{100 + 15}/₁₀₀)

⇒ $8395 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8395

⇒ P = ⁸³⁹⁵/_¹¹⁵/100

⇒ P = 8395 × ¹⁰⁰/₁₁₅

⇒ P = ^{8395 × 100}/₁₁₅

⇒ P = ⁸³⁹⁵⁰⁰/₁₁₅

⇒ P = $7300

Thus, the sum borrowed (P) = $7300 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 8395, then the Principal = ¹⁰⁰/₁₁₅ × 8395

= ^{100 × 8395}/₁₁₅

= ⁸³⁹⁵⁰⁰/₁₁₅

= 7300

Thus, Principal = $7300

Thus, the sum borrowed = $7300 Answer

Similar Questions

(1) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.

(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(6) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.

(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.

(10) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.