Simple Interest
Math MCQs

Question :    William had to pay $3815 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  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $3815

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

$3815 = P (1 + 3% × 3)

⇒ $3815 = P (1 + ³/₁₀₀ × 3)

⇒ $3815 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3815 = P (1 + ⁹/₁₀₀)

⇒ $3815 = P (^{100 + 9}/₁₀₀)

⇒ $3815 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3815

⇒ P = ³⁸¹⁵/_¹⁰⁹/100

⇒ P = 3815 × ¹⁰⁰/₁₀₉

⇒ P = ^{3815 × 100}/₁₀₉

⇒ P = ³⁸¹⁵⁰⁰/₁₀₉

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 3815, then the Principal = ¹⁰⁰/₁₀₉ × 3815

= ^{100 × 3815}/₁₀₉

= ³⁸¹⁵⁰⁰/₁₀₉

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(2) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.

(4) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

(5) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.

(6) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.

(9) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?

(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?