Simple Interest
Math MCQs

Question :    Donald had to pay $4905 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  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $4905

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

$4905 = P (1 + 3% × 3)

⇒ $4905 = P (1 + ³/₁₀₀ × 3)

⇒ $4905 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4905 = P (1 + ⁹/₁₀₀)

⇒ $4905 = P (^{100 + 9}/₁₀₀)

⇒ $4905 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4905

⇒ P = ⁴⁹⁰⁵/_¹⁰⁹/100

⇒ P = 4905 × ¹⁰⁰/₁₀₉

⇒ P = ^{4905 × 100}/₁₀₉

⇒ P = ⁴⁹⁰⁵⁰⁰/₁₀₉

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 4905, then the Principal = ¹⁰⁰/₁₀₉ × 4905

= ^{100 × 4905}/₁₀₉

= ⁴⁹⁰⁵⁰⁰/₁₀₉

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.

(3) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?

(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.

(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(7) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(9) 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.

(10) Lisa had to pay $4657.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.