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) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.

(2) 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?

(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?

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

(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 8% simple interest?

(7) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(8) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.

(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.