Simple Interest
Math MCQs

Question :    How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?

Correct Answer  $7100

Solution & Explanation

Solution

Given,

Amount (A) = $7810

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

$7810 = P (1 + 2% × 5)

⇒ $7810 = P (1 + ²/₁₀₀ × 5)

⇒ $7810 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7810 = P (1 + ¹⁰/₁₀₀)

⇒ $7810 = P (^{100 + 10}/₁₀₀)

⇒ $7810 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7810

⇒ P = ⁷⁸¹⁰/_¹¹⁰/100

⇒ P = 7810 × ¹⁰⁰/₁₁₀

⇒ P = ^{7810 × 100}/₁₁₀

⇒ P = ⁷⁸¹⁰⁰⁰/₁₁₀

⇒ P = $7100

Thus, the sum borrowed (P) = $7100 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 7810, then the Principal = ¹⁰⁰/₁₁₀ × 7810

= ^{100 × 7810}/₁₁₀

= ⁷⁸¹⁰⁰⁰/₁₁₀

= 7100

Thus, Principal = $7100

Thus, the sum borrowed = $7100 Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.

(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6888 to clear the loan, then find the time period of the loan.

(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?

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

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.

(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(7) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.

(9) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.

(10) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.