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) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.

(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.

(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.

(4) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(5) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(7) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.