Simple Interest
Math MCQs

Question :    How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

Correct Answer  $7550

Solution & Explanation

Solution

Given,

Amount (A) = $8305

Rate of Simple Interest (R) = 2%

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

$8305 = P (1 + 2% × 5)

⇒ $8305 = P (1 + ²/₁₀₀ × 5)

⇒ $8305 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8305 = P (1 + ¹⁰/₁₀₀)

⇒ $8305 = P (^{100 + 10}/₁₀₀)

⇒ $8305 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8305

⇒ P = ⁸³⁰⁵/_¹¹⁰/100

⇒ P = 8305 × ¹⁰⁰/₁₁₀

⇒ P = ^{8305 × 100}/₁₁₀

⇒ P = ⁸³⁰⁵⁰⁰/₁₁₀

⇒ P = $7550

Thus, the sum borrowed (P) = $7550 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 8305, then the Principal = ¹⁰⁰/₁₁₀ × 8305

= ^{100 × 8305}/₁₁₀

= ⁸³⁰⁵⁰⁰/₁₁₀

= 7550

Thus, Principal = $7550

Thus, the sum borrowed = $7550 Answer

Similar Questions

(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.

(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?

(5) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.

(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.

(8) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.

(9) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(10) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?