Simple Interest
Math MCQs

Question :    Margaret had to pay $4741.5 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  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $4741.5

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

$4741.5 = P (1 + 3% × 3)

⇒ $4741.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4741.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4741.5 = P (1 + ⁹/₁₀₀)

⇒ $4741.5 = P (^{100 + 9}/₁₀₀)

⇒ $4741.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4741.5

⇒ P = ^4741.5/_¹⁰⁹/100

⇒ P = 4741.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4741.5 × 100}/₁₀₉

⇒ P = ⁴⁷⁴¹⁵⁰/₁₀₉

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 4741.5, then the Principal = ¹⁰⁰/₁₀₉ × 4741.5

= ^{100 × 4741.5}/₁₀₉

= ⁴⁷⁴¹⁵⁰/₁₀₉

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?

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

(3) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.

(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 6% simple interest?

(6) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(8) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?

(9) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.

(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?