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) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.

(3) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?

(5) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(8) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.

(9) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

(10) 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.