Simple Interest
Math MCQs

Question :    If Donald paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $5400

Rate of Simple Interest (R) = 5%

Time (T) = 4 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

$5400 = P (1 + 5% × 4)

⇒ $5400 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5400 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5400 = P (1 + ²⁰/₁₀₀)

⇒ $5400 = P (^{100 + 20}/₁₀₀)

⇒ $5400 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5400

⇒ P = ⁵⁴⁰⁰/_¹²⁰/100

⇒ P = 5400 × ¹⁰⁰/₁₂₀

⇒ P = ^{5400 × 100}/₁₂₀

⇒ P = ⁵⁴⁰⁰⁰⁰/₁₂₀

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 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 5400, then the Principal = ¹⁰⁰/₁₂₀ × 5400

= ^{100 × 5400}/₁₂₀

= ⁵⁴⁰⁰⁰⁰/₁₂₀

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.

(2) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?

(3) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?

(4) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.

(6) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 3 years.

(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.

(9) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?

(10) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.