Simple Interest
Math MCQs

Question :    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?

Correct Answer  $5300

Solution & Explanation

Solution

Given,

Amount (A) = $6360

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

$6360 = P (1 + 4% × 5)

⇒ $6360 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6360 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6360 = P (1 + ²⁰/₁₀₀)

⇒ $6360 = P (^{100 + 20}/₁₀₀)

⇒ $6360 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6360

⇒ P = ⁶³⁶⁰/_¹²⁰/100

⇒ P = 6360 × ¹⁰⁰/₁₂₀

⇒ P = ^{6360 × 100}/₁₂₀

⇒ P = ⁶³⁶⁰⁰⁰/₁₂₀

⇒ P = $5300

Thus, the sum borrowed (P) = $5300 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 6360, then the Principal = ¹⁰⁰/₁₂₀ × 6360

= ^{100 × 6360}/₁₂₀

= ⁶³⁶⁰⁰⁰/₁₂₀

= 5300

Thus, Principal = $5300

Thus, the sum borrowed = $5300 Answer

Similar Questions

(1) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?

(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?

(3) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(4) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.

(7) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?

(9) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.

(10) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.