Simple Interest
Math MCQs

Question :    If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3712

Rate of Simple Interest (R) = 4%

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

$3712 = P (1 + 4% × 4)

⇒ $3712 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3712 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3712 = P (1 + ¹⁶/₁₀₀)

⇒ $3712 = P (^{100 + 16}/₁₀₀)

⇒ $3712 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3712

⇒ P = ³⁷¹²/_¹¹⁶/100

⇒ P = 3712 × ¹⁰⁰/₁₁₆

⇒ P = ^{3712 × 100}/₁₁₆

⇒ P = ³⁷¹²⁰⁰/₁₁₆

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 = 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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 3712, then the Principal = ¹⁰⁰/₁₁₆ × 3712

= ^{100 × 3712}/₁₁₆

= ³⁷¹²⁰⁰/₁₁₆

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.

(3) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.

(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.

(8) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.

(10) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?