Simple Interest
Math MCQs

Question :    Thomas had to pay $4142 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  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4142

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

$4142 = P (1 + 3% × 3)

⇒ $4142 = P (1 + ³/₁₀₀ × 3)

⇒ $4142 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4142 = P (1 + ⁹/₁₀₀)

⇒ $4142 = P (^{100 + 9}/₁₀₀)

⇒ $4142 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4142

⇒ P = ⁴¹⁴²/_¹⁰⁹/100

⇒ P = 4142 × ¹⁰⁰/₁₀₉

⇒ P = ^{4142 × 100}/₁₀₉

⇒ P = ⁴¹⁴²⁰⁰/₁₀₉

⇒ P = $3800

Thus, the sum borrowed (P) = $3800 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 4142, then the Principal = ¹⁰⁰/₁₀₉ × 4142

= ^{100 × 4142}/₁₀₉

= ⁴¹⁴²⁰⁰/₁₀₉

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.

(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?

(4) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.

(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.

(9) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.