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) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(2) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(5) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.

(7) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.

(9) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(10) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.