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) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 7% simple interest?

(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 9% simple interest?

(6) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(7) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?

(9) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.

(10) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?