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) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 4% simple interest?

(3) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?

(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?

(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 2% simple interest?

(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(7) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?

(8) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(9) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.