Simple Interest
Math MCQs

Question :    If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3596

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

$3596 = P (1 + 4% × 4)

⇒ $3596 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3596 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3596 = P (1 + ¹⁶/₁₀₀)

⇒ $3596 = P (^{100 + 16}/₁₀₀)

⇒ $3596 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3596

⇒ P = ³⁵⁹⁶/_¹¹⁶/100

⇒ P = 3596 × ¹⁰⁰/₁₁₆

⇒ P = ^{3596 × 100}/₁₁₆

⇒ P = ³⁵⁹⁶⁰⁰/₁₁₆

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 3596, then the Principal = ¹⁰⁰/₁₁₆ × 3596

= ^{100 × 3596}/₁₁₆

= ³⁵⁹⁶⁰⁰/₁₁₆

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

(1) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?

(3) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.

(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 4% simple interest?

(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?

(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.

(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.

(10) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.