Simple Interest
Math MCQs

Question :    Sandra had to pay $4850.5 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  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $4850.5

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

$4850.5 = P (1 + 3% × 3)

⇒ $4850.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4850.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4850.5 = P (1 + ⁹/₁₀₀)

⇒ $4850.5 = P (^{100 + 9}/₁₀₀)

⇒ $4850.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4850.5

⇒ P = ^4850.5/_¹⁰⁹/100

⇒ P = 4850.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4850.5 × 100}/₁₀₉

⇒ P = ⁴⁸⁵⁰⁵⁰/₁₀₉

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 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 4850.5, then the Principal = ¹⁰⁰/₁₀₉ × 4850.5

= ^{100 × 4850.5}/₁₀₉

= ⁴⁸⁵⁰⁵⁰/₁₀₉

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

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

(2) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(4) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.

(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.

(9) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.