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) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(2) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

(3) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?

(4) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?

(5) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.

(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(10) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.