Simple Interest
Math MCQs

Question :    Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4945

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$4945 = P (1 + 5% × 3)

⇒ $4945 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4945 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4945 = P (1 + ¹⁵/₁₀₀)

⇒ $4945 = P (^{100 + 15}/₁₀₀)

⇒ $4945 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4945

⇒ P = ⁴⁹⁴⁵/_¹¹⁵/100

⇒ P = 4945 × ¹⁰⁰/₁₁₅

⇒ P = ^{4945 × 100}/₁₁₅

⇒ P = ⁴⁹⁴⁵⁰⁰/₁₁₅

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 4945, then the Principal = ¹⁰⁰/₁₁₅ × 4945

= ^{100 × 4945}/₁₁₅

= ⁴⁹⁴⁵⁰⁰/₁₁₅

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(2) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.

(3) If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.

(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?

(6) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?

(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?

(8) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.