Simple Interest
Math MCQs

Question :    How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?

Correct Answer  $7000

Solution & Explanation

Solution

Given,

Amount (A) = $8400

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

$8400 = P (1 + 4% × 5)

⇒ $8400 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8400 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8400 = P (1 + ²⁰/₁₀₀)

⇒ $8400 = P (^{100 + 20}/₁₀₀)

⇒ $8400 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8400

⇒ P = ⁸⁴⁰⁰/_¹²⁰/100

⇒ P = 8400 × ¹⁰⁰/₁₂₀

⇒ P = ^{8400 × 100}/₁₂₀

⇒ P = ⁸⁴⁰⁰⁰⁰/₁₂₀

⇒ 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 = 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 8400, then the Principal = ¹⁰⁰/₁₂₀ × 8400

= ^{100 × 8400}/₁₂₀

= ⁸⁴⁰⁰⁰⁰/₁₂₀

= 7000

Thus, Principal = $7000

Thus, the sum borrowed = $7000 Answer

Similar Questions

(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.

(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 4 years.

(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(4) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?

(6) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.

(8) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.