Simple Interest
Math MCQs

Question :    If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $4380

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

$4380 = P (1 + 5% × 4)

⇒ $4380 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4380 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4380 = P (1 + ²⁰/₁₀₀)

⇒ $4380 = P (^{100 + 20}/₁₀₀)

⇒ $4380 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4380

⇒ P = ⁴³⁸⁰/_¹²⁰/100

⇒ P = 4380 × ¹⁰⁰/₁₂₀

⇒ P = ^{4380 × 100}/₁₂₀

⇒ P = ⁴³⁸⁰⁰⁰/₁₂₀

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 4380, then the Principal = ¹⁰⁰/₁₂₀ × 4380

= ^{100 × 4380}/₁₂₀

= ⁴³⁸⁰⁰⁰/₁₂₀

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.

(2) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.

(3) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.

(5) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.

(6) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.

(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?

(9) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.