Simple Interest
Math MCQs

Question :    Linda had to pay $3651.5 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  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3651.5

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

$3651.5 = P (1 + 3% × 3)

⇒ $3651.5 = P (1 + ³/₁₀₀ × 3)

⇒ $3651.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3651.5 = P (1 + ⁹/₁₀₀)

⇒ $3651.5 = P (^{100 + 9}/₁₀₀)

⇒ $3651.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3651.5

⇒ P = ^3651.5/_¹⁰⁹/100

⇒ P = 3651.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{3651.5 × 100}/₁₀₉

⇒ P = ³⁶⁵¹⁵⁰/₁₀₉

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 3651.5, then the Principal = ¹⁰⁰/₁₀₉ × 3651.5

= ^{100 × 3651.5}/₁₀₉

= ³⁶⁵¹⁵⁰/₁₀₉

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.

(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 3 years.

(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?

(5) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(8) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?

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

(10) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?