Simple Interest
Math MCQs

Question :    Christopher had to pay $4360 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  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4360

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

$4360 = P (1 + 3% × 3)

⇒ $4360 = P (1 + ³/₁₀₀ × 3)

⇒ $4360 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4360 = P (1 + ⁹/₁₀₀)

⇒ $4360 = P (^{100 + 9}/₁₀₀)

⇒ $4360 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4360

⇒ P = ⁴³⁶⁰/_¹⁰⁹/100

⇒ P = 4360 × ¹⁰⁰/₁₀₉

⇒ P = ^{4360 × 100}/₁₀₉

⇒ P = ⁴³⁶⁰⁰⁰/₁₀₉

⇒ P = $4000

Thus, the sum borrowed (P) = $4000 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 4360, then the Principal = ¹⁰⁰/₁₀₉ × 4360

= ^{100 × 4360}/₁₀₉

= ⁴³⁶⁰⁰⁰/₁₀₉

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.

(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.

(3) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.

(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?

(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.

(7) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?

(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?

(10) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.