Simple Interest
Math MCQs

Question :    Betty had to pay $4632.5 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  $4250

Solution & Explanation

Solution

Given,

Amount (A) = $4632.5

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

$4632.5 = P (1 + 3% × 3)

⇒ $4632.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4632.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4632.5 = P (1 + ⁹/₁₀₀)

⇒ $4632.5 = P (^{100 + 9}/₁₀₀)

⇒ $4632.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4632.5

⇒ P = ^4632.5/_¹⁰⁹/100

⇒ P = 4632.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4632.5 × 100}/₁₀₉

⇒ P = ⁴⁶³²⁵⁰/₁₀₉

⇒ P = $4250

Thus, the sum borrowed (P) = $4250 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 4632.5, then the Principal = ¹⁰⁰/₁₀₉ × 4632.5

= ^{100 × 4632.5}/₁₀₉

= ⁴⁶³²⁵⁰/₁₀₉

= 4250

Thus, Principal = $4250

Thus, the sum borrowed = $4250 Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.

(3) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?

(6) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(7) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.

(9) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?

(10) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.