Simple Interest
Math MCQs

Question :    Charles had to pay $4251 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  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4251

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

$4251 = P (1 + 3% × 3)

⇒ $4251 = P (1 + ³/₁₀₀ × 3)

⇒ $4251 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4251 = P (1 + ⁹/₁₀₀)

⇒ $4251 = P (^{100 + 9}/₁₀₀)

⇒ $4251 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4251

⇒ P = ⁴²⁵¹/_¹⁰⁹/100

⇒ P = 4251 × ¹⁰⁰/₁₀₉

⇒ P = ^{4251 × 100}/₁₀₉

⇒ P = ⁴²⁵¹⁰⁰/₁₀₉

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 4251, then the Principal = ¹⁰⁰/₁₀₉ × 4251

= ^{100 × 4251}/₁₀₉

= ⁴²⁵¹⁰⁰/₁₀₉

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer

Similar Questions

(1) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.

(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?

(4) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

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

(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?

(7) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 4 years.

(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?

(9) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.

(10) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.