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) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.

(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.

(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.

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

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

(8) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.

(10) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.