Simple Interest
Math MCQs

Question :    If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $3920

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

$3920 = P (1 + 3% × 4)

⇒ $3920 = P (1 + ³/₁₀₀ × 4)

⇒ $3920 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3920 = P (1 + ¹²/₁₀₀)

⇒ $3920 = P (^{100 + 12}/₁₀₀)

⇒ $3920 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3920

⇒ P = ³⁹²⁰/_¹¹²/100

⇒ P = 3920 × ¹⁰⁰/₁₁₂

⇒ P = ^{3920 × 100}/₁₁₂

⇒ P = ³⁹²⁰⁰⁰/₁₁₂

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 3920, then the Principal = ¹⁰⁰/₁₁₂ × 3920

= ^{100 × 3920}/₁₁₂

= ³⁹²⁰⁰⁰/₁₁₂

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.

(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?

(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.

(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(6) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(7) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(9) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?