Simple Interest
Math MCQs

Question :    If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4700

Solution & Explanation

Solution

Given,

Amount (A) = $5076

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

$5076 = P (1 + 2% × 4)

⇒ $5076 = P (1 + ²/₁₀₀ × 4)

⇒ $5076 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $5076 = P (1 + ⁸/₁₀₀)

⇒ $5076 = P (^{100 + 8}/₁₀₀)

⇒ $5076 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $5076

⇒ P = ⁵⁰⁷⁶/_¹⁰⁸/100

⇒ P = 5076 × ¹⁰⁰/₁₀₈

⇒ P = ^{5076 × 100}/₁₀₈

⇒ P = ⁵⁰⁷⁶⁰⁰/₁₀₈

⇒ P = $4700

Thus, the sum borrowed (P) = $4700 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 5076, then the Principal = ¹⁰⁰/₁₀₈ × 5076

= ^{100 × 5076}/₁₀₈

= ⁵⁰⁷⁶⁰⁰/₁₀₈

= 4700

Thus, Principal = $4700

Thus, the sum borrowed = $4700 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.

(3) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.

(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.

(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?

(7) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.

(8) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.

(9) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(10) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?