Simple Interest
Math MCQs

Question :    Richard had to pay $3924 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  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $3924

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

$3924 = P (1 + 3% × 3)

⇒ $3924 = P (1 + ³/₁₀₀ × 3)

⇒ $3924 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3924 = P (1 + ⁹/₁₀₀)

⇒ $3924 = P (^{100 + 9}/₁₀₀)

⇒ $3924 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3924

⇒ P = ³⁹²⁴/_¹⁰⁹/100

⇒ P = 3924 × ¹⁰⁰/₁₀₉

⇒ P = ^{3924 × 100}/₁₀₉

⇒ P = ³⁹²⁴⁰⁰/₁₀₉

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 3924, then the Principal = ¹⁰⁰/₁₀₉ × 3924

= ^{100 × 3924}/₁₀₉

= ³⁹²⁴⁰⁰/₁₀₉

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.

(2) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?

(3) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.

(5) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 3 years.

(6) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.

(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(9) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.