Simple Interest
Math MCQs

Question :    How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?

Correct Answer  $6050

Solution & Explanation

Solution

Given,

Amount (A) = $6655

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

$6655 = P (1 + 2% × 5)

⇒ $6655 = P (1 + ²/₁₀₀ × 5)

⇒ $6655 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6655 = P (1 + ¹⁰/₁₀₀)

⇒ $6655 = P (^{100 + 10}/₁₀₀)

⇒ $6655 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6655

⇒ P = ⁶⁶⁵⁵/_¹¹⁰/100

⇒ P = 6655 × ¹⁰⁰/₁₁₀

⇒ P = ^{6655 × 100}/₁₁₀

⇒ P = ⁶⁶⁵⁵⁰⁰/₁₁₀

⇒ P = $6050

Thus, the sum borrowed (P) = $6050 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 6655, then the Principal = ¹⁰⁰/₁₁₀ × 6655

= ^{100 × 6655}/₁₁₀

= ⁶⁶⁵⁵⁰⁰/₁₁₀

= 6050

Thus, Principal = $6050

Thus, the sum borrowed = $6050 Answer

Similar Questions

(1) Anthony had to pay $4687 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.

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

(5) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.

(8) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

(9) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?