Simple Interest
Math MCQs

Question :    Donna had to pay $5141 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  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5141

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

$5141 = P (1 + 2% × 3)

⇒ $5141 = P (1 + ²/₁₀₀ × 3)

⇒ $5141 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $5141 = P (1 + ⁶/₁₀₀)

⇒ $5141 = P (^{100 + 6}/₁₀₀)

⇒ $5141 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $5141

⇒ P = ⁵¹⁴¹/_¹⁰⁶/100

⇒ P = 5141 × ¹⁰⁰/₁₀₆

⇒ P = ^{5141 × 100}/₁₀₆

⇒ P = ⁵¹⁴¹⁰⁰/₁₀₆

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5141, then the Principal = ¹⁰⁰/₁₀₆ × 5141

= ^{100 × 5141}/₁₀₆

= ⁵¹⁴¹⁰⁰/₁₀₆

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.

(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.

(4) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(5) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.

(8) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.

(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(10) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?