Simple Interest
Math MCQs

Question :    James had to pay $3270 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  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3270

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

$3270 = P (1 + 3% × 3)

⇒ $3270 = P (1 + ³/₁₀₀ × 3)

⇒ $3270 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3270 = P (1 + ⁹/₁₀₀)

⇒ $3270 = P (^{100 + 9}/₁₀₀)

⇒ $3270 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3270

⇒ P = ³²⁷⁰/_¹⁰⁹/100

⇒ P = 3270 × ¹⁰⁰/₁₀₉

⇒ P = ^{3270 × 100}/₁₀₉

⇒ P = ³²⁷⁰⁰⁰/₁₀₉

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3270, then the Principal = ¹⁰⁰/₁₀₉ × 3270

= ^{100 × 3270}/₁₀₉

= ³²⁷⁰⁰⁰/₁₀₉

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?

(2) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.

(3) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?

(4) In how much time a principal of $3200 will amount to $3328 at a simple interest of 2% per annum?

(5) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.

(6) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.

(9) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.

(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.