Simple Interest
Math MCQs

Question :    How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?

Correct Answer  $5500

Solution & Explanation

Solution

Given,

Amount (A) = $6050

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

$6050 = P (1 + 2% × 5)

⇒ $6050 = P (1 + ²/₁₀₀ × 5)

⇒ $6050 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6050 = P (1 + ¹⁰/₁₀₀)

⇒ $6050 = P (^{100 + 10}/₁₀₀)

⇒ $6050 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6050

⇒ P = ⁶⁰⁵⁰/_¹¹⁰/100

⇒ P = 6050 × ¹⁰⁰/₁₁₀

⇒ P = ^{6050 × 100}/₁₁₀

⇒ P = ⁶⁰⁵⁰⁰⁰/₁₁₀

⇒ P = $5500

Thus, the sum borrowed (P) = $5500 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 6050, then the Principal = ¹⁰⁰/₁₁₀ × 6050

= ^{100 × 6050}/₁₁₀

= ⁶⁰⁵⁰⁰⁰/₁₁₀

= 5500

Thus, Principal = $5500

Thus, the sum borrowed = $5500 Answer

Similar Questions

(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.

(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?

(5) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?

(6) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(7) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(8) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.