Simple Interest
Math MCQs

Question :    How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?

Correct Answer  $5250

Solution & Explanation

Solution

Given,

Amount (A) = $6300

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

$6300 = P (1 + 4% × 5)

⇒ $6300 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6300 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6300 = P (1 + ²⁰/₁₀₀)

⇒ $6300 = P (^{100 + 20}/₁₀₀)

⇒ $6300 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6300

⇒ P = ⁶³⁰⁰/_¹²⁰/100

⇒ P = 6300 × ¹⁰⁰/₁₂₀

⇒ P = ^{6300 × 100}/₁₂₀

⇒ P = ⁶³⁰⁰⁰⁰/₁₂₀

⇒ P = $5250

Thus, the sum borrowed (P) = $5250 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 6300, then the Principal = ¹⁰⁰/₁₂₀ × 6300

= ^{100 × 6300}/₁₂₀

= ⁶³⁰⁰⁰⁰/₁₂₀

= 5250

Thus, Principal = $5250

Thus, the sum borrowed = $5250 Answer

Similar Questions

(1) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.

(3) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.

(5) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?

(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.

(7) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.

(9) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.

(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.