Simple Interest
Math MCQs

Question :    Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $4876

Rate of Simple Interest (R) = 2%

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

$4876 = P (1 + 2% × 3)

⇒ $4876 = P (1 + ²/₁₀₀ × 3)

⇒ $4876 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4876 = P (1 + ⁶/₁₀₀)

⇒ $4876 = P (^{100 + 6}/₁₀₀)

⇒ $4876 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4876

⇒ P = ⁴⁸⁷⁶/_¹⁰⁶/100

⇒ P = 4876 × ¹⁰⁰/₁₀₆

⇒ P = ^{4876 × 100}/₁₀₆

⇒ P = ⁴⁸⁷⁶⁰⁰/₁₀₆

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 4876, then the Principal = ¹⁰⁰/₁₀₆ × 4876

= ^{100 × 4876}/₁₀₆

= ⁴⁸⁷⁶⁰⁰/₁₀₆

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?

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

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?

(4) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?

(6) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(8) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(9) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.