Simple Interest
Math MCQs

Question :    Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3233

Rate of Simple Interest (R) = 2%

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

$3233 = P (1 + 2% × 3)

⇒ $3233 = P (1 + ²/₁₀₀ × 3)

⇒ $3233 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3233 = P (1 + ⁶/₁₀₀)

⇒ $3233 = P (^{100 + 6}/₁₀₀)

⇒ $3233 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3233

⇒ P = ³²³³/_¹⁰⁶/100

⇒ P = 3233 × ¹⁰⁰/₁₀₆

⇒ P = ^{3233 × 100}/₁₀₆

⇒ P = ³²³³⁰⁰/₁₀₆

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3233, then the Principal = ¹⁰⁰/₁₀₆ × 3233

= ^{100 × 3233}/₁₀₆

= ³²³³⁰⁰/₁₀₆

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.

(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(5) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.

(7) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?

(9) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.