Simple Interest
Math MCQs

Question :    Anthony had to pay $4558 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  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4558

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

$4558 = P (1 + 2% × 3)

⇒ $4558 = P (1 + ²/₁₀₀ × 3)

⇒ $4558 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4558 = P (1 + ⁶/₁₀₀)

⇒ $4558 = P (^{100 + 6}/₁₀₀)

⇒ $4558 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4558

⇒ P = ⁴⁵⁵⁸/_¹⁰⁶/100

⇒ P = 4558 × ¹⁰⁰/₁₀₆

⇒ P = ^{4558 × 100}/₁₀₆

⇒ P = ⁴⁵⁵⁸⁰⁰/₁₀₆

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 4558, then the Principal = ¹⁰⁰/₁₀₆ × 4558

= ^{100 × 4558}/₁₀₆

= ⁴⁵⁵⁸⁰⁰/₁₀₆

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.

(2) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.

(4) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?

(5) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.

(8) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.

(9) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.

(10) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.