Simple Interest
Math MCQs

Question :    If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $4320

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

$4320 = P (1 + 5% × 4)

⇒ $4320 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4320 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4320 = P (1 + ²⁰/₁₀₀)

⇒ $4320 = P (^{100 + 20}/₁₀₀)

⇒ $4320 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4320

⇒ P = ⁴³²⁰/_¹²⁰/100

⇒ P = 4320 × ¹⁰⁰/₁₂₀

⇒ P = ^{4320 × 100}/₁₂₀

⇒ P = ⁴³²⁰⁰⁰/₁₂₀

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 4320, then the Principal = ¹⁰⁰/₁₂₀ × 4320

= ^{100 × 4320}/₁₂₀

= ⁴³²⁰⁰⁰/₁₂₀

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.

(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(4) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?

(6) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?

(7) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.

(8) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

(9) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?