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) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?

(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?

(3) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?

(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.

(7) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.

(10) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.