Simple Interest
Math MCQs

Question :    How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

Correct Answer  $5150

Solution & Explanation

Solution

Given,

Amount (A) = $5665

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

$5665 = P (1 + 2% × 5)

⇒ $5665 = P (1 + ²/₁₀₀ × 5)

⇒ $5665 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $5665 = P (1 + ¹⁰/₁₀₀)

⇒ $5665 = P (^{100 + 10}/₁₀₀)

⇒ $5665 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $5665

⇒ P = ⁵⁶⁶⁵/_¹¹⁰/100

⇒ P = 5665 × ¹⁰⁰/₁₁₀

⇒ P = ^{5665 × 100}/₁₁₀

⇒ P = ⁵⁶⁶⁵⁰⁰/₁₁₀

⇒ P = $5150

Thus, the sum borrowed (P) = $5150 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 5665, then the Principal = ¹⁰⁰/₁₁₀ × 5665

= ^{100 × 5665}/₁₁₀

= ⁵⁶⁶⁵⁰⁰/₁₁₀

= 5150

Thus, Principal = $5150

Thus, the sum borrowed = $5150 Answer

Similar Questions

(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.

(2) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

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

(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?

(6) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(8) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(9) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.