Simple Interest
Math MCQs

Question :    If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3950

Solution & Explanation

Solution

Given,

Amount (A) = $4582

Rate of Simple Interest (R) = 4%

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

$4582 = P (1 + 4% × 4)

⇒ $4582 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4582 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4582 = P (1 + ¹⁶/₁₀₀)

⇒ $4582 = P (^{100 + 16}/₁₀₀)

⇒ $4582 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4582

⇒ P = ⁴⁵⁸²/_¹¹⁶/100

⇒ P = 4582 × ¹⁰⁰/₁₁₆

⇒ P = ^{4582 × 100}/₁₁₆

⇒ P = ⁴⁵⁸²⁰⁰/₁₁₆

⇒ P = $3950

Thus, the sum borrowed (P) = $3950 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4582, then the Principal = ¹⁰⁰/₁₁₆ × 4582

= ^{100 × 4582}/₁₁₆

= ⁴⁵⁸²⁰⁰/₁₁₆

= 3950

Thus, Principal = $3950

Thus, the sum borrowed = $3950 Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.

(2) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.

(3) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.

(4) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?

(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.

(8) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(9) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.

(10) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.