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) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(2) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?

(4) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?

(5) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.

(6) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?

(7) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.

(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.