Simple Interest
Math MCQs

Question :    If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3780

Rate of Simple Interest (R) = 5%

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

$3780 = P (1 + 5% × 4)

⇒ $3780 = P (1 + ⁵/₁₀₀ × 4)

⇒ $3780 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $3780 = P (1 + ²⁰/₁₀₀)

⇒ $3780 = P (^{100 + 20}/₁₀₀)

⇒ $3780 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $3780

⇒ P = ³⁷⁸⁰/_¹²⁰/100

⇒ P = 3780 × ¹⁰⁰/₁₂₀

⇒ P = ^{3780 × 100}/₁₂₀

⇒ P = ³⁷⁸⁰⁰⁰/₁₂₀

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 3780, then the Principal = ¹⁰⁰/₁₂₀ × 3780

= ^{100 × 3780}/₁₂₀

= ³⁷⁸⁰⁰⁰/₁₂₀

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(2) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(3) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 3 years.

(5) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.

(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?

(8) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.