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 after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.

(2) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 4 years.

(3) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?

(5) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

(7) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(8) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.