Simple Interest
Math MCQs

Question :    How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?

Correct Answer  $6100

Solution & Explanation

Solution

Given,

Amount (A) = $7320

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

$7320 = P (1 + 4% × 5)

⇒ $7320 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7320 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7320 = P (1 + ²⁰/₁₀₀)

⇒ $7320 = P (^{100 + 20}/₁₀₀)

⇒ $7320 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7320

⇒ P = ⁷³²⁰/_¹²⁰/100

⇒ P = 7320 × ¹⁰⁰/₁₂₀

⇒ P = ^{7320 × 100}/₁₂₀

⇒ P = ⁷³²⁰⁰⁰/₁₂₀

⇒ P = $6100

Thus, the sum borrowed (P) = $6100 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 7320, then the Principal = ¹⁰⁰/₁₂₀ × 7320

= ^{100 × 7320}/₁₂₀

= ⁷³²⁰⁰⁰/₁₂₀

= 6100

Thus, Principal = $6100

Thus, the sum borrowed = $6100 Answer

Similar Questions

(1) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

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

(3) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 6% simple interest?

(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.

(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(7) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.

(9) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.