Simple Interest
Math MCQs

Question :    How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?

Correct Answer  $6900

Solution & Explanation

Solution

Given,

Amount (A) = $8625

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

$8625 = P (1 + 5% × 5)

⇒ $8625 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8625 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8625 = P (1 + ²⁵/₁₀₀)

⇒ $8625 = P (^{100 + 25}/₁₀₀)

⇒ $8625 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8625

⇒ P = ⁸⁶²⁵/_¹²⁵/100

⇒ P = 8625 × ¹⁰⁰/₁₂₅

⇒ P = ^{8625 × 100}/₁₂₅

⇒ P = ⁸⁶²⁵⁰⁰/₁₂₅

⇒ P = $6900

Thus, the sum borrowed (P) = $6900 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 8625, then the Principal = ¹⁰⁰/₁₂₅ × 8625

= ^{100 × 8625}/₁₂₅

= ⁸⁶²⁵⁰⁰/₁₂₅

= 6900

Thus, Principal = $6900

Thus, the sum borrowed = $6900 Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(2) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.

(4) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?

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

(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?

(8) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.

(9) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?

(10) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.