Simple Interest
Math MCQs

Question :    How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?

Correct Answer  $5150

Solution & Explanation

Solution

Given,

Amount (A) = $6437.5

Rate of Simple Interest (R) = 5%

Time (T) = 5 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

$6437.5 = P (1 + 5% × 5)

⇒ $6437.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $6437.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $6437.5 = P (1 + ²⁵/₁₀₀)

⇒ $6437.5 = P (^{100 + 25}/₁₀₀)

⇒ $6437.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $6437.5

⇒ P = ^6437.5/_¹²⁵/100

⇒ P = 6437.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{6437.5 × 100}/₁₂₅

⇒ P = ⁶⁴³⁷⁵⁰/₁₂₅

⇒ P = $5150

Thus, the sum borrowed (P) = $5150 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 6437.5, then the Principal = ¹⁰⁰/₁₂₅ × 6437.5

= ^{100 × 6437.5}/₁₂₅

= ⁶⁴³⁷⁵⁰/₁₂₅

= 5150

Thus, Principal = $5150

Thus, the sum borrowed = $5150 Answer

Similar Questions

(1) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.

(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.

(4) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.

(5) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?

(7) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.

(9) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.