Simple Interest
Math MCQs

Question :    How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?

Correct Answer  $7300

Solution & Explanation

Solution

Given,

Amount (A) = $9125

Rate of Simple Interest (R) = 5%

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

$9125 = P (1 + 5% × 5)

⇒ $9125 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9125 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9125 = P (1 + ²⁵/₁₀₀)

⇒ $9125 = P (^{100 + 25}/₁₀₀)

⇒ $9125 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9125

⇒ P = ⁹¹²⁵/_¹²⁵/100

⇒ P = 9125 × ¹⁰⁰/₁₂₅

⇒ P = ^{9125 × 100}/₁₂₅

⇒ P = ⁹¹²⁵⁰⁰/₁₂₅

⇒ P = $7300

Thus, the sum borrowed (P) = $7300 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 9125, then the Principal = ¹⁰⁰/₁₂₅ × 9125

= ^{100 × 9125}/₁₂₅

= ⁹¹²⁵⁰⁰/₁₂₅

= 7300

Thus, Principal = $7300

Thus, the sum borrowed = $7300 Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(2) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.

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

(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(6) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?

(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.

(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?

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