Simple Interest
Math MCQs

Question :    If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5800

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

$5800 = P (1 + 4% × 4)

⇒ $5800 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5800 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5800 = P (1 + ¹⁶/₁₀₀)

⇒ $5800 = P (^{100 + 16}/₁₀₀)

⇒ $5800 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5800

⇒ P = ⁵⁸⁰⁰/_¹¹⁶/100

⇒ P = 5800 × ¹⁰⁰/₁₁₆

⇒ P = ^{5800 × 100}/₁₁₆

⇒ P = ⁵⁸⁰⁰⁰⁰/₁₁₆

⇒ 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 = 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 5800, then the Principal = ¹⁰⁰/₁₁₆ × 5800

= ^{100 × 5800}/₁₁₆

= ⁵⁸⁰⁰⁰⁰/₁₁₆

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(2) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

(5) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.

(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?

(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 4 years.