Simple Interest
Math MCQs

Question :    How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?

Correct Answer  $7000

Solution & Explanation

Solution

Given,

Amount (A) = $7700

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

$7700 = P (1 + 2% × 5)

⇒ $7700 = P (1 + ²/₁₀₀ × 5)

⇒ $7700 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7700 = P (1 + ¹⁰/₁₀₀)

⇒ $7700 = P (^{100 + 10}/₁₀₀)

⇒ $7700 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7700

⇒ P = ⁷⁷⁰⁰/_¹¹⁰/100

⇒ P = 7700 × ¹⁰⁰/₁₁₀

⇒ P = ^{7700 × 100}/₁₁₀

⇒ P = ⁷⁷⁰⁰⁰⁰/₁₁₀

⇒ P = $7000

Thus, the sum borrowed (P) = $7000 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 7700, then the Principal = ¹⁰⁰/₁₁₀ × 7700

= ^{100 × 7700}/₁₁₀

= ⁷⁷⁰⁰⁰⁰/₁₁₀

= 7000

Thus, Principal = $7000

Thus, the sum borrowed = $7000 Answer

Similar Questions

(1) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(2) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.

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

(5) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(7) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.

(9) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.