Simple Interest
Math MCQs

Question :    Emily had to pay $5177.5 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  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5177.5

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

$5177.5 = P (1 + 3% × 3)

⇒ $5177.5 = P (1 + ³/₁₀₀ × 3)

⇒ $5177.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $5177.5 = P (1 + ⁹/₁₀₀)

⇒ $5177.5 = P (^{100 + 9}/₁₀₀)

⇒ $5177.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $5177.5

⇒ P = ^5177.5/_¹⁰⁹/100

⇒ P = 5177.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{5177.5 × 100}/₁₀₉

⇒ P = ⁵¹⁷⁷⁵⁰/₁₀₉

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5177.5, then the Principal = ¹⁰⁰/₁₀₉ × 5177.5

= ^{100 × 5177.5}/₁₀₉

= ⁵¹⁷⁷⁵⁰/₁₀₉

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.

(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.

(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?

(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?

(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.