Simple Interest
Math MCQs

Question :    Robert had to pay $3379 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  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3379

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

$3379 = P (1 + 3% × 3)

⇒ $3379 = P (1 + ³/₁₀₀ × 3)

⇒ $3379 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3379 = P (1 + ⁹/₁₀₀)

⇒ $3379 = P (^{100 + 9}/₁₀₀)

⇒ $3379 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3379

⇒ P = ³³⁷⁹/_¹⁰⁹/100

⇒ P = 3379 × ¹⁰⁰/₁₀₉

⇒ P = ^{3379 × 100}/₁₀₉

⇒ P = ³³⁷⁹⁰⁰/₁₀₉

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 3379, then the Principal = ¹⁰⁰/₁₀₉ × 3379

= ^{100 × 3379}/₁₀₉

= ³³⁷⁹⁰⁰/₁₀₉

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

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

(2) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?

(3) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.

(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?

(6) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

(7) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.

(9) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(10) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.