Simple Interest
Math MCQs

Question :    How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?

Correct Answer  $5500

Solution & Explanation

Solution

Given,

Amount (A) = $6325

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

$6325 = P (1 + 3% × 5)

⇒ $6325 = P (1 + ³/₁₀₀ × 5)

⇒ $6325 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6325 = P (1 + ¹⁵/₁₀₀)

⇒ $6325 = P (^{100 + 15}/₁₀₀)

⇒ $6325 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6325

⇒ P = ⁶³²⁵/_¹¹⁵/100

⇒ P = 6325 × ¹⁰⁰/₁₁₅

⇒ P = ^{6325 × 100}/₁₁₅

⇒ P = ⁶³²⁵⁰⁰/₁₁₅

⇒ P = $5500

Thus, the sum borrowed (P) = $5500 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 6325, then the Principal = ¹⁰⁰/₁₁₅ × 6325

= ^{100 × 6325}/₁₁₅

= ⁶³²⁵⁰⁰/₁₁₅

= 5500

Thus, Principal = $5500

Thus, the sum borrowed = $5500 Answer

Similar Questions

(1) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.

(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?

(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(5) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

(6) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(8) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?