Simple Interest
Math MCQs

Question :    If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3600

Rate of Simple Interest (R) = 5%

Time (T) = 4 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

$3600 = P (1 + 5% × 4)

⇒ $3600 = P (1 + ⁵/₁₀₀ × 4)

⇒ $3600 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $3600 = P (1 + ²⁰/₁₀₀)

⇒ $3600 = P (^{100 + 20}/₁₀₀)

⇒ $3600 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $3600

⇒ P = ³⁶⁰⁰/_¹²⁰/100

⇒ P = 3600 × ¹⁰⁰/₁₂₀

⇒ P = ^{3600 × 100}/₁₂₀

⇒ P = ³⁶⁰⁰⁰⁰/₁₂₀

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 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 3600, then the Principal = ¹⁰⁰/₁₂₀ × 3600

= ^{100 × 3600}/₁₂₀

= ³⁶⁰⁰⁰⁰/₁₂₀

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.

(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.

(4) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?

(6) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.

(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(8) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.

(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?