Simple Interest
Math MCQs

Question :    How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?

Correct Answer  $5450

Solution & Explanation

Solution

Given,

Amount (A) = $5995

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

$5995 = P (1 + 2% × 5)

⇒ $5995 = P (1 + ²/₁₀₀ × 5)

⇒ $5995 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5995 = P (1 + ¹⁰/₁₀₀)

⇒ $5995 = P (^{100 + 10}/₁₀₀)

⇒ $5995 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5995

⇒ P = ⁵⁹⁹⁵/_¹¹⁰/100

⇒ P = 5995 × ¹⁰⁰/₁₁₀

⇒ P = ^{5995 × 100}/₁₁₀

⇒ P = ⁵⁹⁹⁵⁰⁰/₁₁₀

⇒ P = $5450

Thus, the sum borrowed (P) = $5450 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 5995, then the Principal = ¹⁰⁰/₁₁₀ × 5995

= ^{100 × 5995}/₁₁₀

= ⁵⁹⁹⁵⁰⁰/₁₁₀

= 5450

Thus, Principal = $5450

Thus, the sum borrowed = $5450 Answer

Similar Questions

(1) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.

(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?

(3) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?

(4) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.

(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.

(9) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(10) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?