Simple Interest
Math MCQs

Question :    How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

Correct Answer  $5350

Solution & Explanation

Solution

Given,

Amount (A) = $5885

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

$5885 = P (1 + 2% × 5)

⇒ $5885 = P (1 + ²/₁₀₀ × 5)

⇒ $5885 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5885 = P (1 + ¹⁰/₁₀₀)

⇒ $5885 = P (^{100 + 10}/₁₀₀)

⇒ $5885 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5885

⇒ P = ⁵⁸⁸⁵/_¹¹⁰/100

⇒ P = 5885 × ¹⁰⁰/₁₁₀

⇒ P = ^{5885 × 100}/₁₁₀

⇒ P = ⁵⁸⁸⁵⁰⁰/₁₁₀

⇒ P = $5350

Thus, the sum borrowed (P) = $5350 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 5885, then the Principal = ¹⁰⁰/₁₁₀ × 5885

= ^{100 × 5885}/₁₁₀

= ⁵⁸⁸⁵⁰⁰/₁₁₀

= 5350

Thus, Principal = $5350

Thus, the sum borrowed = $5350 Answer

Similar Questions

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

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.

(3) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?

(4) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(5) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.

(6) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.

(8) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.

(10) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?