Simple Interest
Math MCQs

Question :    How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?

Correct Answer  $5100

Solution & Explanation

Solution

Given,

Amount (A) = $6120

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

$6120 = P (1 + 4% × 5)

⇒ $6120 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6120 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6120 = P (1 + ²⁰/₁₀₀)

⇒ $6120 = P (^{100 + 20}/₁₀₀)

⇒ $6120 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6120

⇒ P = ⁶¹²⁰/_¹²⁰/100

⇒ P = 6120 × ¹⁰⁰/₁₂₀

⇒ P = ^{6120 × 100}/₁₂₀

⇒ P = ⁶¹²⁰⁰⁰/₁₂₀

⇒ P = $5100

Thus, the sum borrowed (P) = $5100 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 6120, then the Principal = ¹⁰⁰/₁₂₀ × 6120

= ^{100 × 6120}/₁₂₀

= ⁶¹²⁰⁰⁰/₁₂₀

= 5100

Thus, Principal = $5100

Thus, the sum borrowed = $5100 Answer

Similar Questions

(1) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 4 years.

(3) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.

(4) If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(7) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(8) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.

(10) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.