Simple Interest
Math MCQs

Question :    If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3720

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

$3720 = P (1 + 5% × 4)

⇒ $3720 = P (1 + ⁵/₁₀₀ × 4)

⇒ $3720 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $3720 = P (1 + ²⁰/₁₀₀)

⇒ $3720 = P (^{100 + 20}/₁₀₀)

⇒ $3720 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $3720

⇒ P = ³⁷²⁰/_¹²⁰/100

⇒ P = 3720 × ¹⁰⁰/₁₂₀

⇒ P = ^{3720 × 100}/₁₂₀

⇒ P = ³⁷²⁰⁰⁰/₁₂₀

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 3720, then the Principal = ¹⁰⁰/₁₂₀ × 3720

= ^{100 × 3720}/₁₂₀

= ³⁷²⁰⁰⁰/₁₂₀

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

(1) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.

(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?

(3) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?

(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(6) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(8) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(9) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.