Simple Interest
Math MCQs

Question :    Patricia had to pay $3433.5 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  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3433.5

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

$3433.5 = P (1 + 3% × 3)

⇒ $3433.5 = P (1 + ³/₁₀₀ × 3)

⇒ $3433.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3433.5 = P (1 + ⁹/₁₀₀)

⇒ $3433.5 = P (^{100 + 9}/₁₀₀)

⇒ $3433.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3433.5

⇒ P = ^3433.5/_¹⁰⁹/100

⇒ P = 3433.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{3433.5 × 100}/₁₀₉

⇒ P = ³⁴³³⁵⁰/₁₀₉

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 3433.5, then the Principal = ¹⁰⁰/₁₀₉ × 3433.5

= ^{100 × 3433.5}/₁₀₉

= ³⁴³³⁵⁰/₁₀₉

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.

(2) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?

(3) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.

(6) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.

(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.