Simple Interest
Math MCQs

Question :    How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $6000

Rate of Simple Interest (R) = 4%

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

$6000 = P (1 + 4% × 5)

⇒ $6000 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6000 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6000 = P (1 + ²⁰/₁₀₀)

⇒ $6000 = P (^{100 + 20}/₁₀₀)

⇒ $6000 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6000

⇒ P = ⁶⁰⁰⁰/_¹²⁰/100

⇒ P = 6000 × ¹⁰⁰/₁₂₀

⇒ P = ^{6000 × 100}/₁₂₀

⇒ P = ⁶⁰⁰⁰⁰⁰/₁₂₀

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 6000, then the Principal = ¹⁰⁰/₁₂₀ × 6000

= ^{100 × 6000}/₁₂₀

= ⁶⁰⁰⁰⁰⁰/₁₂₀

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.

(2) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) 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?

(4) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?

(5) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?

(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

(7) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 4 years.

(8) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(10) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?