Simple Interest
Math MCQs

Question :    If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $5280

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

$5280 = P (1 + 5% × 4)

⇒ $5280 = P (1 + ⁵/₁₀₀ × 4)

⇒ $5280 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $5280 = P (1 + ²⁰/₁₀₀)

⇒ $5280 = P (^{100 + 20}/₁₀₀)

⇒ $5280 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $5280

⇒ P = ⁵²⁸⁰/_¹²⁰/100

⇒ P = 5280 × ¹⁰⁰/₁₂₀

⇒ P = ^{5280 × 100}/₁₂₀

⇒ P = ⁵²⁸⁰⁰⁰/₁₂₀

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 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 5280, then the Principal = ¹⁰⁰/₁₂₀ × 5280

= ^{100 × 5280}/₁₂₀

= ⁵²⁸⁰⁰⁰/₁₂₀

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

(1) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?

(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(3) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(4) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(6) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.

(8) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.

(9) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(10) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.