Simple Interest
Math MCQs

Question :    Charles had to pay $4485 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  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4485

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

$4485 = P (1 + 5% × 3)

⇒ $4485 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4485 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4485 = P (1 + ¹⁵/₁₀₀)

⇒ $4485 = P (^{100 + 15}/₁₀₀)

⇒ $4485 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4485

⇒ P = ⁴⁴⁸⁵/_¹¹⁵/100

⇒ P = 4485 × ¹⁰⁰/₁₁₅

⇒ P = ^{4485 × 100}/₁₁₅

⇒ P = ⁴⁴⁸⁵⁰⁰/₁₁₅

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 4485, then the Principal = ¹⁰⁰/₁₁₅ × 4485

= ^{100 × 4485}/₁₁₅

= ⁴⁴⁸⁵⁰⁰/₁₁₅

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer

Similar Questions

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

(2) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.

(3) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?

(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?

(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.

(8) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?

(9) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.

(10) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.