Simple Interest
Math MCQs

Question :    How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?

Correct Answer  $5150

Solution & Explanation

Solution

Given,

Amount (A) = $5922.5

Rate of Simple Interest (R) = 3%

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

$5922.5 = P (1 + 3% × 5)

⇒ $5922.5 = P (1 + ³/₁₀₀ × 5)

⇒ $5922.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $5922.5 = P (1 + ¹⁵/₁₀₀)

⇒ $5922.5 = P (^{100 + 15}/₁₀₀)

⇒ $5922.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5922.5

⇒ P = ^5922.5/_¹¹⁵/100

⇒ P = 5922.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{5922.5 × 100}/₁₁₅

⇒ P = ⁵⁹²²⁵⁰/₁₁₅

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 5922.5, then the Principal = ¹⁰⁰/₁₁₅ × 5922.5

= ^{100 × 5922.5}/₁₁₅

= ⁵⁹²²⁵⁰/₁₁₅

= 5150

Thus, Principal = $5150

Thus, the sum borrowed = $5150 Answer

Similar Questions

(1) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.

(3) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.

(6) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.

(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?

(9) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

(10) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?