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) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.

(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?

(5) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.

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

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.

(9) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.