Simple Interest
Math MCQs

Question :    If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $5040

Rate of Simple Interest (R) = 3%

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

$5040 = P (1 + 3% × 4)

⇒ $5040 = P (1 + ³/₁₀₀ × 4)

⇒ $5040 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5040 = P (1 + ¹²/₁₀₀)

⇒ $5040 = P (^{100 + 12}/₁₀₀)

⇒ $5040 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5040

⇒ P = ⁵⁰⁴⁰/_¹¹²/100

⇒ P = 5040 × ¹⁰⁰/₁₁₂

⇒ P = ^{5040 × 100}/₁₁₂

⇒ P = ⁵⁰⁴⁰⁰⁰/₁₁₂

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 5040, then the Principal = ¹⁰⁰/₁₁₂ × 5040

= ^{100 × 5040}/₁₁₂

= ⁵⁰⁴⁰⁰⁰/₁₁₂

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.

(2) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.

(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?

(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?

(6) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?

(9) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?