Simple Interest
Math MCQs

Question :    How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?

Correct Answer  $6100

Solution & Explanation

Solution

Given,

Amount (A) = $6710

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

$6710 = P (1 + 2% × 5)

⇒ $6710 = P (1 + ²/₁₀₀ × 5)

⇒ $6710 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6710 = P (1 + ¹⁰/₁₀₀)

⇒ $6710 = P (^{100 + 10}/₁₀₀)

⇒ $6710 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6710

⇒ P = ⁶⁷¹⁰/_¹¹⁰/100

⇒ P = 6710 × ¹⁰⁰/₁₁₀

⇒ P = ^{6710 × 100}/₁₁₀

⇒ P = ⁶⁷¹⁰⁰⁰/₁₁₀

⇒ P = $6100

Thus, the sum borrowed (P) = $6100 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 6710, then the Principal = ¹⁰⁰/₁₁₀ × 6710

= ^{100 × 6710}/₁₁₀

= ⁶⁷¹⁰⁰⁰/₁₁₀

= 6100

Thus, Principal = $6100

Thus, the sum borrowed = $6100 Answer

Similar Questions

(1) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?

(2) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.

(4) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.

(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.

(6) If Margaret paid $5046 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.

(10) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.