Simple Interest
Math MCQs

Question :    How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?

Correct Answer  $7150

Solution & Explanation

Solution

Given,

Amount (A) = $8580

Rate of Simple Interest (R) = 4%

Time (T) = 5 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

$8580 = P (1 + 4% × 5)

⇒ $8580 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8580 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8580 = P (1 + ²⁰/₁₀₀)

⇒ $8580 = P (^{100 + 20}/₁₀₀)

⇒ $8580 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8580

⇒ P = ⁸⁵⁸⁰/_¹²⁰/100

⇒ P = 8580 × ¹⁰⁰/₁₂₀

⇒ P = ^{8580 × 100}/₁₂₀

⇒ P = ⁸⁵⁸⁰⁰⁰/₁₂₀

⇒ P = $7150

Thus, the sum borrowed (P) = $7150 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8580, then the Principal = ¹⁰⁰/₁₂₀ × 8580

= ^{100 × 8580}/₁₂₀

= ⁸⁵⁸⁰⁰⁰/₁₂₀

= 7150

Thus, Principal = $7150

Thus, the sum borrowed = $7150 Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.

(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?

(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(5) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(6) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.

(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.