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) How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?

(2) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 3 years.

(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 7 years.

(5) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?

(8) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.

(10) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.