Simple Interest
Math MCQs

Question :    How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?

Correct Answer  $5550

Solution & Explanation

Solution

Given,

Amount (A) = $6105

Rate of Simple Interest (R) = 2%

Time (T) = 5 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

$6105 = P (1 + 2% × 5)

⇒ $6105 = P (1 + ²/₁₀₀ × 5)

⇒ $6105 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6105 = P (1 + ¹⁰/₁₀₀)

⇒ $6105 = P (^{100 + 10}/₁₀₀)

⇒ $6105 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6105

⇒ P = ⁶¹⁰⁵/_¹¹⁰/100

⇒ P = 6105 × ¹⁰⁰/₁₁₀

⇒ P = ^{6105 × 100}/₁₁₀

⇒ P = ⁶¹⁰⁵⁰⁰/₁₁₀

⇒ P = $5550

Thus, the sum borrowed (P) = $5550 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 6105, then the Principal = ¹⁰⁰/₁₁₀ × 6105

= ^{100 × 6105}/₁₁₀

= ⁶¹⁰⁵⁰⁰/₁₁₀

= 5550

Thus, Principal = $5550

Thus, the sum borrowed = $5550 Answer

Similar Questions

(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

(2) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 3 years.

(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.

(5) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.

(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.

(9) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.

(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.