Simple Interest
Math MCQs

Question :    Donna had to pay $5577.5 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  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5577.5

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

$5577.5 = P (1 + 5% × 3)

⇒ $5577.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5577.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5577.5 = P (1 + ¹⁵/₁₀₀)

⇒ $5577.5 = P (^{100 + 15}/₁₀₀)

⇒ $5577.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5577.5

⇒ P = ^5577.5/_¹¹⁵/100

⇒ P = 5577.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{5577.5 × 100}/₁₁₅

⇒ P = ⁵⁵⁷⁷⁵⁰/₁₁₅

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5577.5, then the Principal = ¹⁰⁰/₁₁₅ × 5577.5

= ^{100 × 5577.5}/₁₁₅

= ⁵⁵⁷⁷⁵⁰/₁₁₅

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

(1) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?

(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?

(5) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(6) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?

(8) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?