Simple Interest
Math MCQs

Question :    How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

Correct Answer  $7450

Solution & Explanation

Solution

Given,

Amount (A) = $8940

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

$8940 = P (1 + 4% × 5)

⇒ $8940 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8940 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8940 = P (1 + ²⁰/₁₀₀)

⇒ $8940 = P (^{100 + 20}/₁₀₀)

⇒ $8940 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8940

⇒ P = ⁸⁹⁴⁰/_¹²⁰/100

⇒ P = 8940 × ¹⁰⁰/₁₂₀

⇒ P = ^{8940 × 100}/₁₂₀

⇒ P = ⁸⁹⁴⁰⁰⁰/₁₂₀

⇒ P = $7450

Thus, the sum borrowed (P) = $7450 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 8940, then the Principal = ¹⁰⁰/₁₂₀ × 8940

= ^{100 × 8940}/₁₂₀

= ⁸⁹⁴⁰⁰⁰/₁₂₀

= 7450

Thus, Principal = $7450

Thus, the sum borrowed = $7450 Answer

Similar Questions

(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?

(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(3) Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 4 years.

(7) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(8) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.

(10) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.