Simple Interest
Math MCQs

Question :    Joseph had to pay $4033 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  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $4033

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

$4033 = P (1 + 3% × 3)

⇒ $4033 = P (1 + ³/₁₀₀ × 3)

⇒ $4033 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4033 = P (1 + ⁹/₁₀₀)

⇒ $4033 = P (^{100 + 9}/₁₀₀)

⇒ $4033 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4033

⇒ P = ⁴⁰³³/_¹⁰⁹/100

⇒ P = 4033 × ¹⁰⁰/₁₀₉

⇒ P = ^{4033 × 100}/₁₀₉

⇒ P = ⁴⁰³³⁰⁰/₁₀₉

⇒ P = $3700

Thus, the sum borrowed (P) = $3700 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 4033, then the Principal = ¹⁰⁰/₁₀₉ × 4033

= ^{100 × 4033}/₁₀₉

= ⁴⁰³³⁰⁰/₁₀₉

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

(2) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?

(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?

(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?

(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?

(6) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.

(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?

(8) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.

(10) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.