Simple Interest
Math MCQs

Question :    Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $3924

Rate of Simple Interest (R) = 3%

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

$3924 = P (1 + 3% × 3)

⇒ $3924 = P (1 + ³/₁₀₀ × 3)

⇒ $3924 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3924 = P (1 + ⁹/₁₀₀)

⇒ $3924 = P (^{100 + 9}/₁₀₀)

⇒ $3924 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3924

⇒ P = ³⁹²⁴/_¹⁰⁹/100

⇒ P = 3924 × ¹⁰⁰/₁₀₉

⇒ P = ^{3924 × 100}/₁₀₉

⇒ P = ³⁹²⁴⁰⁰/₁₀₉

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 = 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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 3924, then the Principal = ¹⁰⁰/₁₀₉ × 3924

= ^{100 × 3924}/₁₀₉

= ³⁹²⁴⁰⁰/₁₀₉

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?

(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.

(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

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

(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.