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) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.

(2) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.

(4) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?

(6) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.

(8) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?

(10) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?