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) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.

(3) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?

(4) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(5) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(6) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(7) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 7% simple interest?

(8) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.

(10) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.