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) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(2) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.

(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.

(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(5) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?

(6) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(7) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(9) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?