Simple Interest
Math MCQs

Question :    Michelle had to pay $5395.5 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  $4950

Solution & Explanation

Solution

Given,

Amount (A) = $5395.5

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

$5395.5 = P (1 + 3% × 3)

⇒ $5395.5 = P (1 + ³/₁₀₀ × 3)

⇒ $5395.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $5395.5 = P (1 + ⁹/₁₀₀)

⇒ $5395.5 = P (^{100 + 9}/₁₀₀)

⇒ $5395.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $5395.5

⇒ P = ^5395.5/_¹⁰⁹/100

⇒ P = 5395.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{5395.5 × 100}/₁₀₉

⇒ P = ⁵³⁹⁵⁵⁰/₁₀₉

⇒ P = $4950

Thus, the sum borrowed (P) = $4950 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 5395.5, then the Principal = ¹⁰⁰/₁₀₉ × 5395.5

= ^{100 × 5395.5}/₁₀₉

= ⁵³⁹⁵⁵⁰/₁₀₉

= 4950

Thus, Principal = $4950

Thus, the sum borrowed = $4950 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.

(3) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.

(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.

(6) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.

(8) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.

(10) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.