Simple Interest
Math MCQs

Question :    How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?

Correct Answer  $6250

Solution & Explanation

Solution

Given,

Amount (A) = $7500

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

$7500 = P (1 + 4% × 5)

⇒ $7500 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7500 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7500 = P (1 + ²⁰/₁₀₀)

⇒ $7500 = P (^{100 + 20}/₁₀₀)

⇒ $7500 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7500

⇒ P = ⁷⁵⁰⁰/_¹²⁰/100

⇒ P = 7500 × ¹⁰⁰/₁₂₀

⇒ P = ^{7500 × 100}/₁₂₀

⇒ P = ⁷⁵⁰⁰⁰⁰/₁₂₀

⇒ P = $6250

Thus, the sum borrowed (P) = $6250 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 7500, then the Principal = ¹⁰⁰/₁₂₀ × 7500

= ^{100 × 7500}/₁₂₀

= ⁷⁵⁰⁰⁰⁰/₁₂₀

= 6250

Thus, Principal = $6250

Thus, the sum borrowed = $6250 Answer

Similar Questions

(1) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.

(2) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(4) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.

(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.

(9) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?

(10) 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.