Simple Interest
Math MCQs

Question :    Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5450

Rate of Simple Interest (R) = 3%

Time (T) = 3 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

$5450 = P (1 + 3% × 3)

⇒ $5450 = P (1 + ³/₁₀₀ × 3)

⇒ $5450 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $5450 = P (1 + ⁹/₁₀₀)

⇒ $5450 = P (^{100 + 9}/₁₀₀)

⇒ $5450 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $5450

⇒ P = ⁵⁴⁵⁰/_¹⁰⁹/100

⇒ P = 5450 × ¹⁰⁰/₁₀₉

⇒ P = ^{5450 × 100}/₁₀₉

⇒ P = ⁵⁴⁵⁰⁰⁰/₁₀₉

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 5450, then the Principal = ¹⁰⁰/₁₀₉ × 5450

= ^{100 × 5450}/₁₀₉

= ⁵⁴⁵⁰⁰⁰/₁₀₉

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.

(2) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?

(3) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?

(4) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.

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

(7) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.