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) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?

(2) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?

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

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.

(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(6) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?

(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.

(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.