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) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.

(3) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.

(7) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?

(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.