Simple Interest
Math MCQs

Question :    How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?

Correct Answer  $5450

Solution & Explanation

Solution

Given,

Amount (A) = $6540

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

$6540 = P (1 + 4% × 5)

⇒ $6540 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6540 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6540 = P (1 + ²⁰/₁₀₀)

⇒ $6540 = P (^{100 + 20}/₁₀₀)

⇒ $6540 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6540

⇒ P = ⁶⁵⁴⁰/_¹²⁰/100

⇒ P = 6540 × ¹⁰⁰/₁₂₀

⇒ P = ^{6540 × 100}/₁₂₀

⇒ P = ⁶⁵⁴⁰⁰⁰/₁₂₀

⇒ P = $5450

Thus, the sum borrowed (P) = $5450 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 6540, then the Principal = ¹⁰⁰/₁₂₀ × 6540

= ^{100 × 6540}/₁₂₀

= ⁶⁵⁴⁰⁰⁰/₁₂₀

= 5450

Thus, Principal = $5450

Thus, the sum borrowed = $5450 Answer

Similar Questions

(1) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.

(2) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.

(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?

(7) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.

(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.

(10) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?