Simple Interest
Math MCQs

Question :    How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?

Correct Answer  $5150

Solution & Explanation

Solution

Given,

Amount (A) = $6180

Rate of Simple Interest (R) = 4%

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

$6180 = P (1 + 4% × 5)

⇒ $6180 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6180 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6180 = P (1 + ²⁰/₁₀₀)

⇒ $6180 = P (^{100 + 20}/₁₀₀)

⇒ $6180 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6180

⇒ P = ⁶¹⁸⁰/_¹²⁰/100

⇒ P = 6180 × ¹⁰⁰/₁₂₀

⇒ P = ^{6180 × 100}/₁₂₀

⇒ P = ⁶¹⁸⁰⁰⁰/₁₂₀

⇒ P = $5150

Thus, the sum borrowed (P) = $5150 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 6180, then the Principal = ¹⁰⁰/₁₂₀ × 6180

= ^{100 × 6180}/₁₂₀

= ⁶¹⁸⁰⁰⁰/₁₂₀

= 5150

Thus, Principal = $5150

Thus, the sum borrowed = $5150 Answer

Similar Questions

(1) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 8% simple interest for 8 years.

(3) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.

(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.

(6) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.

(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?

(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.