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) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.

(3) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.

(5) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.

(6) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.

(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

(8) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(9) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.