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) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?

(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.

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

(6) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.

(7) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?

(8) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(10) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.