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) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(2) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?

(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?

(4) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.

(5) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(7) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 8 years.

(9) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.