Simple Interest
Math MCQs

Question :    If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $4080

Rate of Simple Interest (R) = 5%

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

$4080 = P (1 + 5% × 4)

⇒ $4080 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4080 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4080 = P (1 + ²⁰/₁₀₀)

⇒ $4080 = P (^{100 + 20}/₁₀₀)

⇒ $4080 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4080

⇒ P = ⁴⁰⁸⁰/_¹²⁰/100

⇒ P = 4080 × ¹⁰⁰/₁₂₀

⇒ P = ^{4080 × 100}/₁₂₀

⇒ P = ⁴⁰⁸⁰⁰⁰/₁₂₀

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 4080, then the Principal = ¹⁰⁰/₁₂₀ × 4080

= ^{100 × 4080}/₁₂₀

= ⁴⁰⁸⁰⁰⁰/₁₂₀

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.

(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?

(3) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(4) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(5) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?

(7) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?

(8) 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.

(9) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?