Simple Interest
Math MCQs

Question :    If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5130

Rate of Simple Interest (R) = 2%

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

$5130 = P (1 + 2% × 4)

⇒ $5130 = P (1 + ²/₁₀₀ × 4)

⇒ $5130 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $5130 = P (1 + ⁸/₁₀₀)

⇒ $5130 = P (^{100 + 8}/₁₀₀)

⇒ $5130 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $5130

⇒ P = ⁵¹³⁰/_¹⁰⁸/100

⇒ P = 5130 × ¹⁰⁰/₁₀₈

⇒ P = ^{5130 × 100}/₁₀₈

⇒ P = ⁵¹³⁰⁰⁰/₁₀₈

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 5130, then the Principal = ¹⁰⁰/₁₀₈ × 5130

= ^{100 × 5130}/₁₀₈

= ⁵¹³⁰⁰⁰/₁₀₈

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?

(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(4) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(5) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.

(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.

(9) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(10) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.