Simple Interest
Math MCQs

Question :    Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $4950

Solution & Explanation

Solution

Given,

Amount (A) = $5692.5

Rate of Simple Interest (R) = 5%

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

$5692.5 = P (1 + 5% × 3)

⇒ $5692.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5692.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5692.5 = P (1 + ¹⁵/₁₀₀)

⇒ $5692.5 = P (^{100 + 15}/₁₀₀)

⇒ $5692.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5692.5

⇒ P = ^5692.5/_¹¹⁵/100

⇒ P = 5692.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{5692.5 × 100}/₁₁₅

⇒ P = ⁵⁶⁹²⁵⁰/₁₁₅

⇒ 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 15

Thus, simple interest for 3 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 5692.5, then the Principal = ¹⁰⁰/₁₁₅ × 5692.5

= ^{100 × 5692.5}/₁₁₅

= ⁵⁶⁹²⁵⁰/₁₁₅

= 4950

Thus, Principal = $4950

Thus, the sum borrowed = $4950 Answer

Similar Questions

(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 9% simple interest?

(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.

(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(4) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?

(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

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

(9) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.