Simple Interest
Math MCQs

Question :    If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $5096

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

$5096 = P (1 + 3% × 4)

⇒ $5096 = P (1 + ³/₁₀₀ × 4)

⇒ $5096 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5096 = P (1 + ¹²/₁₀₀)

⇒ $5096 = P (^{100 + 12}/₁₀₀)

⇒ $5096 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5096

⇒ P = ⁵⁰⁹⁶/_¹¹²/100

⇒ P = 5096 × ¹⁰⁰/₁₁₂

⇒ P = ^{5096 × 100}/₁₁₂

⇒ P = ⁵⁰⁹⁶⁰⁰/₁₁₂

⇒ P = $4550

Thus, the sum borrowed (P) = $4550 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 5096, then the Principal = ¹⁰⁰/₁₁₂ × 5096

= ^{100 × 5096}/₁₁₂

= ⁵⁰⁹⁶⁰⁰/₁₁₂

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.

(2) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.

(4) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.

(7) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

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

(9) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.

(10) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?