Simple Interest
Math MCQs

Question :    Linda had to pay $3852.5 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  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3852.5

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

$3852.5 = P (1 + 5% × 3)

⇒ $3852.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $3852.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $3852.5 = P (1 + ¹⁵/₁₀₀)

⇒ $3852.5 = P (^{100 + 15}/₁₀₀)

⇒ $3852.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $3852.5

⇒ P = ^3852.5/_¹¹⁵/100

⇒ P = 3852.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{3852.5 × 100}/₁₁₅

⇒ P = ³⁸⁵²⁵⁰/₁₁₅

⇒ 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 = 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 3852.5, then the Principal = ¹⁰⁰/₁₁₅ × 3852.5

= ^{100 × 3852.5}/₁₁₅

= ³⁸⁵²⁵⁰/₁₁₅

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(2) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?

(3) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(5) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(6) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(8) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(9) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?