Simple Interest
Math MCQs

Question :    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.

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5400

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

$5400 = P (1 + 2% × 4)

⇒ $5400 = P (1 + ²/₁₀₀ × 4)

⇒ $5400 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $5400 = P (1 + ⁸/₁₀₀)

⇒ $5400 = P (^{100 + 8}/₁₀₀)

⇒ $5400 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $5400

⇒ P = ⁵⁴⁰⁰/_¹⁰⁸/100

⇒ P = 5400 × ¹⁰⁰/₁₀₈

⇒ P = ^{5400 × 100}/₁₀₈

⇒ P = ⁵⁴⁰⁰⁰⁰/₁₀₈

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 5400, then the Principal = ¹⁰⁰/₁₀₈ × 5400

= ^{100 × 5400}/₁₀₈

= ⁵⁴⁰⁰⁰⁰/₁₀₈

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.

(2) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.

(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?

(5) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.

(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?

(9) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.