Simple Interest
Math MCQs

Question :    How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?

Correct Answer  $5650

Solution & Explanation

Solution

Given,

Amount (A) = $6780

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

$6780 = P (1 + 4% × 5)

⇒ $6780 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6780 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6780 = P (1 + ²⁰/₁₀₀)

⇒ $6780 = P (^{100 + 20}/₁₀₀)

⇒ $6780 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6780

⇒ P = ⁶⁷⁸⁰/_¹²⁰/100

⇒ P = 6780 × ¹⁰⁰/₁₂₀

⇒ P = ^{6780 × 100}/₁₂₀

⇒ P = ⁶⁷⁸⁰⁰⁰/₁₂₀

⇒ P = $5650

Thus, the sum borrowed (P) = $5650 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 6780, then the Principal = ¹⁰⁰/₁₂₀ × 6780

= ^{100 × 6780}/₁₂₀

= ⁶⁷⁸⁰⁰⁰/₁₂₀

= 5650

Thus, Principal = $5650

Thus, the sum borrowed = $5650 Answer

Similar Questions

(1) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.

(2) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(4) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.

(7) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?

(9) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?

(10) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.