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) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?

(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(3) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.

(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 9% simple interest?

(7) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?