Simple Interest
Math MCQs

Question :    How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?

Correct Answer  $5450

Solution & Explanation

Solution

Given,

Amount (A) = $6267.5

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

$6267.5 = P (1 + 3% × 5)

⇒ $6267.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6267.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6267.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6267.5 = P (^{100 + 15}/₁₀₀)

⇒ $6267.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6267.5

⇒ P = ^6267.5/_¹¹⁵/100

⇒ P = 6267.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6267.5 × 100}/₁₁₅

⇒ P = ⁶²⁶⁷⁵⁰/₁₁₅

⇒ 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 = 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 6267.5, then the Principal = ¹⁰⁰/₁₁₅ × 6267.5

= ^{100 × 6267.5}/₁₁₅

= ⁶²⁶⁷⁵⁰/₁₁₅

= 5450

Thus, Principal = $5450

Thus, the sum borrowed = $5450 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.

(3) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(4) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(5) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.

(6) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.

(8) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.

(10) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.