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) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.

(3) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(4) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(5) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.

(8) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?

(10) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.