Simple Interest
Math MCQs

Question :    Daniel had to pay $4469 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  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4469

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

$4469 = P (1 + 3% × 3)

⇒ $4469 = P (1 + ³/₁₀₀ × 3)

⇒ $4469 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4469 = P (1 + ⁹/₁₀₀)

⇒ $4469 = P (^{100 + 9}/₁₀₀)

⇒ $4469 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4469

⇒ P = ⁴⁴⁶⁹/_¹⁰⁹/100

⇒ P = 4469 × ¹⁰⁰/₁₀₉

⇒ P = ^{4469 × 100}/₁₀₉

⇒ P = ⁴⁴⁶⁹⁰⁰/₁₀₉

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 4469, then the Principal = ¹⁰⁰/₁₀₉ × 4469

= ^{100 × 4469}/₁₀₉

= ⁴⁴⁶⁹⁰⁰/₁₀₉

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.

(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.

(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.

(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(7) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.

(8) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?

(9) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?

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