Simple Interest
Math MCQs

Question :    How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?

Correct Answer  $6900

Solution & Explanation

Solution

Given,

Amount (A) = $7590

Rate of Simple Interest (R) = 2%

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

$7590 = P (1 + 2% × 5)

⇒ $7590 = P (1 + ²/₁₀₀ × 5)

⇒ $7590 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7590 = P (1 + ¹⁰/₁₀₀)

⇒ $7590 = P (^{100 + 10}/₁₀₀)

⇒ $7590 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7590

⇒ P = ⁷⁵⁹⁰/_¹¹⁰/100

⇒ P = 7590 × ¹⁰⁰/₁₁₀

⇒ P = ^{7590 × 100}/₁₁₀

⇒ P = ⁷⁵⁹⁰⁰⁰/₁₁₀

⇒ 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7590, then the Principal = ¹⁰⁰/₁₁₀ × 7590

= ^{100 × 7590}/₁₁₀

= ⁷⁵⁹⁰⁰⁰/₁₁₀

= 6900

Thus, Principal = $6900

Thus, the sum borrowed = $6900 Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.

(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.

(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.

(5) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

(7) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.

(9) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?

(10) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.