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) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(4) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?

(5) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?

(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(9) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(10) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 6% simple interest?