Simple Interest
Math MCQs

Question :    Margaret had to pay $4741.5 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  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $4741.5

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

$4741.5 = P (1 + 3% × 3)

⇒ $4741.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4741.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4741.5 = P (1 + ⁹/₁₀₀)

⇒ $4741.5 = P (^{100 + 9}/₁₀₀)

⇒ $4741.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4741.5

⇒ P = ^4741.5/_¹⁰⁹/100

⇒ P = 4741.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4741.5 × 100}/₁₀₉

⇒ P = ⁴⁷⁴¹⁵⁰/₁₀₉

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 4741.5, then the Principal = ¹⁰⁰/₁₀₉ × 4741.5

= ^{100 × 4741.5}/₁₀₉

= ⁴⁷⁴¹⁵⁰/₁₀₉

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?

(2) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?

(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?

(4) 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.

(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?

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

(7) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.

(9) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.

(10) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.