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) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?

(2) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.

(3) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(4) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.

(7) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?

(8) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(9) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?

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