Simple Interest
Math MCQs

Question :    How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?

Correct Answer  $7750

Solution & Explanation

Solution

Given,

Amount (A) = $9300

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

$9300 = P (1 + 4% × 5)

⇒ $9300 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9300 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9300 = P (1 + ²⁰/₁₀₀)

⇒ $9300 = P (^{100 + 20}/₁₀₀)

⇒ $9300 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9300

⇒ P = ⁹³⁰⁰/_¹²⁰/100

⇒ P = 9300 × ¹⁰⁰/₁₂₀

⇒ P = ^{9300 × 100}/₁₂₀

⇒ P = ⁹³⁰⁰⁰⁰/₁₂₀

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 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 9300, then the Principal = ¹⁰⁰/₁₂₀ × 9300

= ^{100 × 9300}/₁₂₀

= ⁹³⁰⁰⁰⁰/₁₂₀

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer

Similar Questions

(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.

(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(4) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.

(5) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?

(8) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.

(10) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.